What is the integral of (3x-7)sin(5x+2) ?

The integral of (3x-7)sin(5x+2) is -1/5 cos(5x+2)(3x-7)+3/25 sin(5x+2)+C

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integral of (3x-7)sin(5x+2)

\int (3 x - 7) sin (5 x + 2) d x

- \frac{1}{5} cos (5 x + 2) (3 x - 7) + \frac{3}{25} sin (5 x + 2) + C

Solution steps

\int (3 x - 7) sin (5 x + 2) d x

Apply Integration By Parts

: - \frac{1}{5} cos (5 x + 2) (3 x - 7) - \int - \frac{3}{5} cos (5 x + 2) d x

= - \frac{1}{5} cos (5 x + 2) (3 x - 7) - \int - \frac{3}{5} cos (5 x + 2) d x

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

= - \frac{1}{5} cos (5 x + 2) (3 x - 7) - (- \frac{3}{25} sin (5 x + 2))

Simplify

= - \frac{1}{5} cos (5 x + 2) (3 x - 7) + \frac{3}{25} sin (5 x + 2)

Add a constant to the solution

= - \frac{1}{5} cos (5 x + 2) (3 x - 7) + \frac{3}{25} sin (5 x + 2) + C

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

\int 1 - 64 x^{2} d x

\frac{d}{d x} (\frac{x ln ( x )}{1 + ln ( x )})

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

\frac{d}{d t} (2)

What is the integral of (3x-7)sin(5x+2) ?
The integral of (3x-7)sin(5x+2) is -1/5 cos(5x+2)(3x-7)+3/25 sin(5x+2)+C