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Identical expressions
sin(x^ six)*x^ five
sinus of (x to the power of 6) multiply by x to the power of 5
sinus of (x to the power of six) multiply by x to the power of five
sin(x6)*x5
sinx6*x5
sin(x⁶)*x⁵
sin(x^6)x^5
sin(x6)x5
sinx6x5
sinx^6x^5
sin(x^6)*x^5dx

Integral of sin(x^6)*x^5 dx

The solution

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  0              
  /              
 |               
 |     / 6\  5   
 |  sin\x /*x  dx
 |               
/                
0

$$\int\limits_{0}^{0} x^{5} \sin{\left(x^{6} \right)}\, dx$$

Integral(sin(x^6)*x^5, (x, 0, 0))

Detail solution

Let $u = x^{6}$ .

Then let $du = 6 x^{5} dx$ and substitute $\frac{du}{6}$ :

$\int \frac{\sin{\left(u \right)}}{6}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{6}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{6}$
Now substitute $u$ back in:

$- \frac{\cos{\left(x^{6} \right)}}{6}$
Add the constant of integration:

$- \frac{\cos{\left(x^{6} \right)}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(x^{6} \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                        / 6\
 |    / 6\  5          cos\x /
 | sin\x /*x  dx = C - -------
 |                        6   
/

$$\int x^{5} \sin{\left(x^{6} \right)}\, dx = C - \frac{\cos{\left(x^{6} \right)}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Integral of sin(x^6)*x^5 dx

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The solution