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

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

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∫01x2sin⁡(x3)1 dx\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

  1. Let u=x3u = x^{3}.

    Then let du=3x2dxdu = 3 x^{2} dx and substitute du3\frac{du}{3}:

    ∫sin⁡(u)9 du\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:

      ∫sin⁡(u)3 du=∫sin⁡(u) du3\int \frac{\sin{\left(u \right)}}{3}\, du = \frac{\int \sin{\left(u \right)}\, du}{3}

      1. The integral of sine is negative cosine:

        ∫sin⁡(u) du=−cos⁡(u)\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}

      So, the result is: −cos⁡(u)3- \frac{\cos{\left(u \right)}}{3}

    Now substitute uu back in:

    −cos⁡(x3)3- \frac{\cos{\left(x^{3} \right)}}{3}

  2. Add the constant of integration:

    −cos⁡(x3)3+constant- \frac{\cos{\left(x^{3} \right)}}{3}+ \mathrm{constant}

The answer is:

−cos⁡(x3)3+constant- \frac{\cos{\left(x^{3} \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫x2sin⁡(x3)1 dx=C−cos⁡(x3)3\int x^{2} \sin{\left(x^{3} \right)} 1\, dx = C - \frac{\cos{\left(x^{3} \right)}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-1
Plot the graph f(x)
The answer [src] 
1   cos(1)
- - ------
3     3
13−cos⁡(1)3\frac{1}{3} - \frac{\cos{\left(1 \right)}}{3} 
=
= 
1   cos(1)
- - ------
3     3
13−cos⁡(1)3\frac{1}{3} - \frac{\cos{\left(1 \right)}}{3}
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Numerical answer [src] 
0.15323256471062
0.15323256471062
The graph
Integral of x^2sin(x^3)dx dx

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

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