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Solving integrals/ x^2sin(x^3)dx

Integral of x^2sin(x^3)dx dx

The solution

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  1                
  /                
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 |   2    / 3\     
 |  x *sin\x /*1 dx
 |                 
/                  
0

$$\int\limits_{0}^{1} x^{2} \sin{\left(x^{3} \right)} 1\, dx$$

Integral(x^2*sin(x^3)*1, (x, 0, 1))

Detail solution

Let $u = x^{3}$ .

Then let $du = 3 x^{2} dx$ and substitute $\frac{du}{3}$ :

$\int \frac{\sin{\left(u \right)}}{9}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{3}\, du = \frac{\int \sin{\left(u \right)}\, du}{3}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{3}$
Now substitute $u$ back in:

$- \frac{\cos{\left(x^{3} \right)}}{3}$
Add the constant of integration:

$- \frac{\cos{\left(x^{3} \right)}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(x^{3} \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                          / 3\
 |  2    / 3\            cos\x /
 | x *sin\x /*1 dx = C - -------
 |                          3   
/

$$\int x^{2} \sin{\left(x^{3} \right)} 1\, dx = C - \frac{\cos{\left(x^{3} \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   cos(1)
- - ------
3     3

$$\frac{1}{3} - \frac{\cos{\left(1 \right)}}{3}$$

1   cos(1)
- - ------
3     3

$$\frac{1}{3} - \frac{\cos{\left(1 \right)}}{3}$$

Упростить

Numerical answer [src]

0.15323256471062

0.15323256471062

The graph

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

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Identical expressions

Integral of x^2sin(x^3)dx dx

Limits of integration:

The graph:

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The solution