What is the integral of 15x^3cos(5x^4+11) ?

The integral of 15x^3cos(5x^4+11) is 3/4 sin(5x^4+11)+C

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integral of 15x^3cos(5x^4+11)

\int 15 x^{3} cos (5 x^{4} + 11) d x

\frac{3}{4} sin (5 x^{4} + 11) + C

Solution steps

\int 15 x^{3} cos (5 x^{4} + 11) d x

Take the constant out:

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

= 15 \cdot \int x^{3} cos (5 x^{4} + 11) d x

Apply u-substitution

: \int \frac{cos ( u )}{20} d u

= 15 \cdot \int \frac{cos ( u )}{20} d u

Take the constant out:

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

= 15 \cdot \frac{1}{20} \cdot \int cos (u) d u

Use the common integral:

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

= 15 \cdot \frac{1}{20} sin (u)

Substitute back

u = 5 x^{4} + 11

= 15 \cdot \frac{1}{20} sin (5 x^{4} + 11)

Simplify

15 \cdot \frac{1}{20} sin (5 x^{4} + 11) : \frac{3}{4} sin (5 x^{4} + 11)

= \frac{3}{4} sin (5 x^{4} + 11)

Add a constant to the solution

= \frac{3}{4} sin (5 x^{4} + 11) + C

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What is the integral of 15x^3cos(5x^4+11) ?
The integral of 15x^3cos(5x^4+11) is 3/4 sin(5x^4+11)+C