Get the solution to "Find ∫2x3cos⁡(x2)dx"

Joni Kenny

Answered question

2021-08-18

Find

\int 2 x^{3} \cos (x^{2}) d x

Brittany Patton

Skilled2021-08-19Added 100 answers

We have to find the following integral

\int 2 x^{3} \cos (x^{2}) d x

Substitute

u = x^{2}

we have

d u = 2 x d x

Thus we have
int

2 x^{3} \cos (x^{2}) d x = \int u \cos (u) d u

u \sin (u) - \int \sin (u) d u

[Using integration by parts]
=

x^{2} \sin (x^{2}) - (- \cos (x^{2})) + C

\int 2 x^{3} \cos (x^{2}) d x = x^{2} \sin (x^{2}) - (- \cos (x^{2})) + C

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