What is the integral of (3-2x)cos(5-4x) ?

The integral of (3-2x)cos(5-4x) is -1/4 sin(5-4x)(3-2x)-1/8 cos(5-4x)+C

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integral of (3-2x)cos(5-4x)

\int (3 - 2 x) cos (5 - 4 x) d x

- \frac{1}{4} sin (5 - 4 x) (3 - 2 x) - \frac{1}{8} cos (5 - 4 x) + C

Solution steps

\int (3 - 2 x) cos (5 - 4 x) d x

Apply Integration By Parts

: - \frac{1}{4} sin (5 - 4 x) (3 - 2 x) - \int \frac{1}{2} sin (5 - 4 x) d x

= - \frac{1}{4} sin (5 - 4 x) (3 - 2 x) - \int \frac{1}{2} sin (5 - 4 x) d x

\int \frac{1}{2} sin (5 - 4 x) d x = \frac{1}{8} cos (5 - 4 x)

= - \frac{1}{4} sin (5 - 4 x) (3 - 2 x) - \frac{1}{8} cos (5 - 4 x)

Add a constant to the solution

= - \frac{1}{4} sin (5 - 4 x) (3 - 2 x) - \frac{1}{8} cos (5 - 4 x) + C

\int 2^{5 t^{2}} t d t

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\int \frac{x}{x ^{2} + 2} 7^{l n (x^{2} + 2)} d x

\int \frac{x}{( 5 x ^{2} + 1 ) ^{2}} d x

What is the integral of (3-2x)cos(5-4x) ?
The integral of (3-2x)cos(5-4x) is -1/4 sin(5-4x)(3-2x)-1/8 cos(5-4x)+C