What is the integral of 3xsin(7x) ?

The integral of 3xsin(7x) is 3(-1/7 xcos(7x)+1/49 sin(7x))+C

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integral of 3xsin(7x)

\int 3 x sin (7 x) d x

3 (- \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x)) + C

Solution steps

\int 3 x sin (7 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x sin (7 x) d x

Apply Integration By Parts

: - \frac{1}{7} x cos (7 x) - \int - \frac{1}{7} cos (7 x) d x

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

\int - \frac{1}{7} cos (7 x) d x = - \frac{1}{49} sin (7 x)

= 3 (- \frac{1}{7} x cos (7 x) - (- \frac{1}{49} sin (7 x)))

Simplify

= 3 (- \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x))

Add a constant to the solution

= 3 (- \frac{1}{7} x cos (7 x) + \frac{1}{49} sin (7 x)) + C

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What is the integral of 3xsin(7x) ?
The integral of 3xsin(7x) is 3(-1/7 xcos(7x)+1/49 sin(7x))+C