What is the integral of x^3(cos(x^4+2)) ?

The integral of x^3(cos(x^4+2)) is 1/4 sin(x^4+2)+C

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integral of x^3(cos(x^4+2))

\int x^{3} (cos (x^{4} + 2)) d x

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

Solution steps

\int x^{3} cos (x^{4} + 2) d x

Apply u-substitution

= \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 = x^{4} + 2

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

Add a constant to the solution

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

What is the integral of x^3(cos(x^4+2)) ?
The integral of x^3(cos(x^4+2)) is 1/4 sin(x^4+2)+C