What is the integral of xcos(x^2+5) ?

The integral of xcos(x^2+5) is 1/2 sin(x^2+5)+C

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integral of xcos(x^2+5)

\int x cos (x^{2} + 5) d x

\frac{1}{2} sin (x^{2} + 5) + C

Solution steps

\int x cos (x^{2} + 5) d x

Apply u-substitution

: \int \frac{cos ( u )}{2} d u

= \int \frac{cos ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{2} sin (u)

Substitute back

u = x^{2} + 5

= \frac{1}{2} sin (x^{2} + 5)

Add a constant to the solution

= \frac{1}{2} sin (x^{2} + 5) + C

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What is the integral of xcos(x^2+5) ?
The integral of xcos(x^2+5) is 1/2 sin(x^2+5)+C