What is the integral of (3x^2+5)sin(x^3+5x-12) ?

The integral of (3x^2+5)sin(x^3+5x-12) is -cos(x^3+5x-12)+C

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integral of (3x^2+5)sin(x^3+5x-12)

\int (3 x^{2} + 5) sin (x^{3} + 5 x - 12) d x

- cos (x^{3} + 5 x - 12) + C

Solution steps

\int (3 x^{2} + 5) sin (x^{3} + 5 x - 12) d x

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

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

= - cos (u)

Substitute back

u = x^{3} + 5 x - 12

= - cos (x^{3} + 5 x - 12)

Add a constant to the solution

= - cos (x^{3} + 5 x - 12) + C

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What is the integral of (3x^2+5)sin(x^3+5x-12) ?
The integral of (3x^2+5)sin(x^3+5x-12) is -cos(x^3+5x-12)+C