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Identical expressions
two x^ seven +3x^2- one + six ^x
2x to the power of 7 plus 3x squared minus 1 plus 6 to the power of x
two x to the power of seven plus 3x squared minus one plus six to the power of x
2x7+3x2-1+6x
2x⁷+3x²-1+6^x
2x to the power of 7+3x to the power of 2-1+6 to the power of x
2x^7+3x^2-1+6^xdx
Similar expressions
2x^7+3x^2+1+6^x
2x^7+3x^2-1-6^x
2x^7-3x^2-1+6^x

Solving integrals/ 2x^7+3x^2-1+6^x

Integral of 2x^7+3x^2-1+6^x dx

The solution

You have entered [src]

  1                          
  /                          
 |                           
 |  /   7      2        x\   
 |  \2*x  + 3*x  - 1 + 6 / dx
 |                           
/                            
0

$$\int\limits_{0}^{1} \left(6^{x} + \left(\left(2 x^{7} + 3 x^{2}\right) - 1\right)\right)\, dx$$

Integral(2*x^7 + 3*x^2 - 1 + 6^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.
  
  $\int 6^{x}\, dx = \frac{6^{x}}{\log{\left(6 \right)}}$
1. Integrate term-by-term:
  1. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 2 x^{7}\, dx = 2 \int x^{7}\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{7}\, dx = \frac{x^{8}}{8}$
      So, the result is: $\frac{x^{8}}{4}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{2}\, dx = \frac{x^{3}}{3}$
      So, the result is: $x^{3}$
    The result is: $\frac{x^{8}}{4} + x^{3}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-1\right)\, dx = - x$
  The result is: $\frac{x^{8}}{4} + x^{3} - x$
The result is: $\frac{6^{x}}{\log{\left(6 \right)}} + \frac{x^{8}}{4} + x^{3} - x$
Add the constant of integration:

$\frac{6^{x}}{\log{\left(6 \right)}} + \frac{x^{8}}{4} + x^{3} - x+ \mathrm{constant}$

The answer is:

$\frac{6^{x}}{\log{\left(6 \right)}} + \frac{x^{8}}{4} + x^{3} - x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                    
 |                                           8      x  
 | /   7      2        x\           3       x      6   
 | \2*x  + 3*x  - 1 + 6 / dx = C + x  - x + -- + ------
 |                                          4    log(6)
/

$$\int \left(6^{x} + \left(\left(2 x^{7} + 3 x^{2}\right) - 1\right)\right)\, dx = \frac{6^{x}}{\log{\left(6 \right)}} + C + \frac{x^{8}}{4} + x^{3} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1     5   
- + ------
4   log(6)

$$\frac{1}{4} + \frac{5}{\log{\left(6 \right)}}$$

1     5   
- + ------
4   log(6)

$$\frac{1}{4} + \frac{5}{\log{\left(6 \right)}}$$

1/4 + 5/log(6)

Numerical answer [src]

3.04055313275624

3.04055313275624

The graph

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

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Integral of 2x^7+3x^2-1+6^x dx

Limits of integration:

The graph:

Piecewise:

The solution