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

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

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integral of (2x-3)sin(x^2-3x)

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

- cos (x^{2} - 3 x) + C

Solution steps

\int (2 x - 3) sin (x^{2} - 3 x) 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^{2} - 3 x

= - cos (x^{2} - 3 x)

Add a constant to the solution

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

\int (e^{- x} + e^{- 2 x}) d x

\int 5^{2 x + 1} d x

\int e^{x} + x^{e} d x

\int \frac{1}{4 - 2 x} d x

\int 6 x e^{x^{3}} d x

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