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Identical expressions
((e^x)+(one /((cos^ two)x))+(one /(sqrt(ten +(x^ two))))+ nine ^x)
((e to the power of x) plus (1 divide by (( co sinus of e of squared )x)) plus (1 divide by ( square root of (10 plus (x squared )))) plus 9 to the power of x)
((e to the power of x) plus (one divide by (( co sinus of e of to the power of two)x)) plus (one divide by ( square root of (ten plus (x to the power of two)))) plus nine to the power of x)
((e^x)+(1/((cos^2)x))+(1/(√(10+(x^2))))+9^x)
((ex)+(1/((cos2)x))+(1/(sqrt(10+(x2))))+9x)
ex+1/cos2x+1/sqrt10+x2+9x
((e^x)+(1/((cos²)x))+(1/(sqrt(10+(x²))))+9^x)
((e to the power of x)+(1/((cos to the power of 2)x))+(1/(sqrt(10+(x to the power of 2))))+9 to the power of x)
e^x+1/cos^2x+1/sqrt10+x^2+9^x
((e^x)+(1 divide by ((cos^2)x))+(1 divide by (sqrt(10+(x^2))))+9^x)
((e^x)+(1/((cos^2)x))+(1/(sqrt(10+(x^2))))+9^x)dx
Similar expressions
((e^x)+(1/((cos^2)x))+(1/(sqrt(10-(x^2))))+9^x)
((e^x)-(1/((cos^2)x))+(1/(sqrt(10+(x^2))))+9^x)
((e^x)+(1/((cos^2)x))+(1/(sqrt(10+(x^2))))-9^x)
((e^x)+(1/((cos^2)x))-(1/(sqrt(10+(x^2))))+9^x)

Solving integrals/ ((e^x)+(1/((cos^2)x))+(1/(sqrt(10+(x^2))))+9^x)

Integral of ((e^x)+(1/((cos^2)x))+(1/(sqrt(10+(x^2))))+9^x) dx

The solution

You have entered [src]

  1                                        
  /                                        
 |                                         
 |  / x       1            1          x\   
 |  |E  + --------- + ------------ + 9 | dx
 |  |        2           _________     |   
 |  |     cos (x)*x     /       2      |   
 |  \                 \/  10 + x       /   
 |                                         
/                                          
0

$$\int\limits_{0}^{1} \left(9^{x} + \left(\left(e^{x} + \frac{1}{x \cos^{2}{\left(x \right)}}\right) + \frac{1}{\sqrt{x^{2} + 10}}\right)\right)\, dx$$

Integral(E^x + 1/(cos(x)^2*x) + 1/(sqrt(10 + x^2)) + 9^x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of an exponential function is itself divided by the natural logarithm of the base.
  
  $\int 9^{x}\, dx = \frac{9^{x}}{\log{\left(9 \right)}}$
1. Integrate term-by-term:
  1. Integrate term-by-term:
    1. The integral of the exponential function is itself.
      
      $\int e^{x}\, dx = e^{x}$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx$
    The result is: $e^{x} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx$
  The result is: $e^{x} + \log{\left(\frac{\sqrt{10} x}{10} + \sqrt{\frac{x^{2}}{10} + 1} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx$
The result is: $\frac{9^{x}}{\log{\left(9 \right)}} + e^{x} + \log{\left(\frac{\sqrt{10} x}{10} + \sqrt{\frac{x^{2}}{10} + 1} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx$
Now simplify:

$\frac{9^{x} + \left(e^{x} + \log{\left(\frac{\sqrt{10} \left(x + \sqrt{x^{2} + 10}\right)}{10} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx\right) \log{\left(9 \right)}}{\log{\left(9 \right)}}$
Add the constant of integration:

$\frac{9^{x} + \left(e^{x} + \log{\left(\frac{\sqrt{10} \left(x + \sqrt{x^{2} + 10}\right)}{10} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx\right) \log{\left(9 \right)}}{\log{\left(9 \right)}}+ \mathrm{constant}$

The answer is:

$\frac{9^{x} + \left(e^{x} + \log{\left(\frac{\sqrt{10} \left(x + \sqrt{x^{2} + 10}\right)}{10} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx\right) \log{\left(9 \right)}}{\log{\left(9 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                              /                  /     ________           \
 |                                                       x      |                   |    /      2        ____|
 | / x       1            1          x\           x     9       |     1             |   /      x     x*\/ 10 |
 | |E  + --------- + ------------ + 9 | dx = C + E  + ------ +  | --------- dx + log|  /   1 + --  + --------|
 | |        2           _________     |               log(9)    |      2            \\/        10       10   /
 | |     cos (x)*x     /       2      |                         | x*cos (x)                                   
 | \                 \/  10 + x       /                         |                                             
 |                                                             /                                              
/

$$\int \left(9^{x} + \left(\left(e^{x} + \frac{1}{x \cos^{2}{\left(x \right)}}\right) + \frac{1}{\sqrt{x^{2} + 10}}\right)\right)\, dx = \frac{9^{x}}{\log{\left(9 \right)}} + e^{x} + C + \log{\left(\frac{\sqrt{10} x}{10} + \sqrt{\frac{x^{2}}{10} + 1} \right)} + \int \frac{1}{x \cos^{2}{\left(x \right)}}\, dx$$

Simplify

The answer [src]

  1                                                                                    
  /                                                                                    
 |                                                                                     
 |     _________                       _________                _________              
 |    /       2         2         x   /       2     2          /       2     2     x   
 |  \/  10 + x   + x*cos (x) + x*9 *\/  10 + x  *cos (x) + x*\/  10 + x  *cos (x)*e    
 |  -------------------------------------------------------------------------------- dx
 |                                    _________                                        
 |                                   /       2     2                                   
 |                               x*\/  10 + x  *cos (x)                                
 |                                                                                     
/                                                                                      
0

$$\int\limits_{0}^{1} \frac{9^{x} x \sqrt{x^{2} + 10} \cos^{2}{\left(x \right)} + x \sqrt{x^{2} + 10} e^{x} \cos^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + \sqrt{x^{2} + 10}}{x \sqrt{x^{2} + 10} \cos^{2}{\left(x \right)}}\, dx$$

  1                                                                                    
  /                                                                                    
 |                                                                                     
 |     _________                       _________                _________              
 |    /       2         2         x   /       2     2          /       2     2     x   
 |  \/  10 + x   + x*cos (x) + x*9 *\/  10 + x  *cos (x) + x*\/  10 + x  *cos (x)*e    
 |  -------------------------------------------------------------------------------- dx
 |                                    _________                                        
 |                                   /       2     2                                   
 |                               x*\/  10 + x  *cos (x)                                
 |                                                                                     
/                                                                                      
0

Integral((sqrt(10 + x^2) + x*cos(x)^2 + x*9^x*sqrt(10 + x^2)*cos(x)^2 + x*sqrt(10 + x^2)*cos(x)^2*exp(x))/(x*sqrt(10 + x^2)*cos(x)^2), (x, 0, 1))

Numerical answer [src]

50.531349750937

50.531349750937

Use the examples entering the upper and lower limits of integration.

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Integral of ((e^x)+(1/((cos^2)x))+(1/(sqrt(10+(x^2))))+9^x) dx

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