What is the integral of x^4cos(6x^5+3) ?

The integral of x^4cos(6x^5+3) is 1/30 sin(6x^5+3)+C

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integral of x^4cos(6x^5+3)

\int x^{4} cos (6 x^{5} + 3) d x

\frac{1}{30} sin (6 x^{5} + 3) + C

Solution steps

\int x^{4} cos (6 x^{5} + 3) d x

Apply u-substitution

: \int \frac{cos ( u )}{30} d u

= \int \frac{cos ( u )}{30} d u

Take the constant out:

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

= \frac{1}{30} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{30} sin (u)

Substitute back

u = 6 x^{5} + 3

= \frac{1}{30} sin (6 x^{5} + 3)

Add a constant to the solution

= \frac{1}{30} sin (6 x^{5} + 3) + C

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\int \frac{16 x ^{2}}{25 - 36 x ^{6}} d x

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What is the integral of x^4cos(6x^5+3) ?
The integral of x^4cos(6x^5+3) is 1/30 sin(6x^5+3)+C