What is the integral of (6x-5)cos(3x^2-5x) ?

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

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integral of (6x-5)cos(3x^2-5x)

\int (6 x - 5) cos (3 x^{2} - 5 x) d x

sin (3 x^{2} - 5 x) + C

Solution steps

\int (6 x - 5) cos (3 x^{2} - 5 x) d x

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = 3 x^{2} - 5 x

= sin (3 x^{2} - 5 x)

Add a constant to the solution

= sin (3 x^{2} - 5 x) + C

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