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Integral of d{x}:
Integral of e^(x^2)
Integral of e^(-x)
Integral of sin(x)^3
Integral of cos(x/2)
Identical expressions
one /x^ eight - one /cosx+ four ^x- one /x^ two - twenty-five
1 divide by x to the power of 8 minus 1 divide by co sinus of e of x plus 4 to the power of x minus 1 divide by x squared minus 25
one divide by x to the power of eight minus one divide by co sinus of e of x plus four to the power of x minus one divide by x to the power of two minus twenty minus five
1/x8-1/cosx+4x-1/x2-25
1/x⁸-1/cosx+4^x-1/x²-25
1/x to the power of 8-1/cosx+4 to the power of x-1/x to the power of 2-25
1 divide by x^8-1 divide by cosx+4^x-1 divide by x^2-25
1/x^8-1/cosx+4^x-1/x^2-25dx
Similar expressions
1/x^8+1/cosx+4^x-1/x^2-25
1/x^8-1/cosx+4^x+1/x^2-25
1/x^8-1/cosx-4^x-1/x^2-25
1/x^8-1/cosx+4^x-1/x^2+25

Solving integrals/ 1/x^8-1/cosx+4^x-1/x^2-25

Integral of 1/x^8-1/cosx+4^x-1/x^2-25 dx

The solution

You have entered [src]

  1                                
  /                                
 |                                 
 |  /1      1       x   1      \   
 |  |-- - ------ + 4  - -- - 25| dx
 |  | 8   cos(x)         2     |   
 |  \x                  x      /   
 |                                 
/                                  
0

$$\int\limits_{0}^{1} \left(\left(\left(4^{x} + \left(- \frac{1}{\cos{\left(x \right)}} + \frac{1}{x^{8}}\right)\right) - \frac{1}{x^{2}}\right) - 25\right)\, dx$$

Integral(1/(x^8) - 1/cos(x) + 4^x - 1/x^2 - 25, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. Integrate term-by-term:
    1. The integral of an exponential function is itself divided by the natural logarithm of the base.
      
      $\int 4^{x}\, dx = \frac{4^{x}}{\log{\left(4 \right)}}$
    1. Integrate term-by-term:
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\int \left(- \frac{1}{\cos{\left(x \right)}}\right)\, dx = - \int \frac{1}{\cos{\left(x \right)}}\, dx$
        
        Don't know the steps in finding this integral.
        
        But the integral is
        
        $- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}$
        
        So, the result is: $\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2}$
      1. Don't know the steps in finding this integral.
        
        But the integral is
        
        $- \frac{1}{7 x^{7}}$
      The result is: $\frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \frac{1}{7 x^{7}}$
    The result is: $\frac{4^{x}}{\log{\left(4 \right)}} + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \frac{1}{7 x^{7}}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{x^{2}}\right)\, dx = - \int \frac{1}{x^{2}}\, dx$
    So, the result is: $\text{NaN}$
  The result is: $\text{NaN}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-25\right)\, dx = - 25 x$
The result is: $\text{NaN}$
Add the constant of integration:

$\text{NaN}+ \mathrm{constant}$

The answer is:

$\text{NaN}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 | /1      1       x   1      \         
 | |-- - ------ + 4  - -- - 25| dx = nan
 | | 8   cos(x)         2     |         
 | \x                  x      /         
 |                                      
/

$$\int \left(\left(\left(4^{x} + \left(- \frac{1}{\cos{\left(x \right)}} + \frac{1}{x^{8}}\right)\right) - \frac{1}{x^{2}}\right) - 25\right)\, dx = \text{NaN}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     pi*I
oo + ----
      2

$$\infty + \frac{i \pi}{2}$$

     pi*I
oo + ----
      2

$$\infty + \frac{i \pi}{2}$$

oo + pi*i/2

Numerical answer [src]

6.80884325415506e+132

6.80884325415506e+132

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

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Integral of 1/x^8-1/cosx+4^x-1/x^2-25 dx

Limits of integration:

The graph:

Piecewise:

The solution