What is the integral of cos(3x^2+5)x ?

The integral of cos(3x^2+5)x is 1/6 sin(3x^2+5)+C

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integral of cos(3x^2+5)x

\int cos (3 x^{2} + 5) x d x

\frac{1}{6} sin (3 x^{2} + 5) + C

Solution steps

\int cos (3 x^{2} + 5) x d x

Apply u-substitution

= \int \frac{cos ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{6} sin (u)

Substitute back

u = 3 x^{2} + 5

= \frac{1}{6} sin (3 x^{2} + 5)

Add a constant to the solution

= \frac{1}{6} sin (3 x^{2} + 5) + C

What is the integral of cos(3x^2+5)x ?
The integral of cos(3x^2+5)x is 1/6 sin(3x^2+5)+C