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

The integral of (3-2x)sin(5x) is -3/5 cos(5x)-2(-1/5 xcos(5x)+1/25 sin(5x))+C

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integral of (3-2x)sin(5x)

\int (3 - 2 x) sin (5 x) d x

- \frac{3}{5} cos (5 x) - 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x)) + C

Solution steps

\int (3 - 2 x) sin (5 x) d x

Expand

(3 - 2 x) sin (5 x) : 3 sin (5 x) - 2 x sin (5 x)

= \int 3 sin (5 x) - 2 x sin (5 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 sin (5 x) d x - \int 2 x sin (5 x) d x

\int 3 sin (5 x) d x = - \frac{3}{5} cos (5 x)

\int 2 x sin (5 x) d x = 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x))

= - \frac{3}{5} cos (5 x) - 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x))

Add a constant to the solution

= - \frac{3}{5} cos (5 x) - 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x)) + C

\int cot (9 x) d x

y = x^{5} \cdot e^{x}

\frac{d}{d x} (2 (3^{- x})^{2} + lo g_{2} (x^{4} - 1))

e^{1 - 2 t} + cos^{2} (t)

f (x) = \frac{18 x + 8 x ^{2}}{( 9 + 8 x ) ^{2}}

What is the integral of (3-2x)sin(5x) ?
The integral of (3-2x)sin(5x) is -3/5 cos(5x)-2(-1/5 xcos(5x)+1/25 sin(5x))+C