What is the integral of xcos(2x^2+7)dx ?

The integral of xcos(2x^2+7)dx is 1/4 sin(2x^2+7)+C

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integral of xcos(2x^2+7)dx

integral

x cos (2 x^{2} + 7) d x

\frac{1}{4} sin (2 x^{2} + 7) + C

Solution steps

\int x cos (2 x^{2} + 7) d x

Apply u-substitution

: \int \frac{cos ( u )}{4} d u

= \int \frac{cos ( u )}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{4} sin (u)

Substitute back

u = 2 x^{2} + 7

= \frac{1}{4} sin (2 x^{2} + 7)

Add a constant to the solution

= \frac{1}{4} sin (2 x^{2} + 7) + C

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What is the integral of xcos(2x^2+7)dx ?
The integral of xcos(2x^2+7)dx is 1/4 sin(2x^2+7)+C