What is the integral of 2xsin(6x) ?

The integral of 2xsin(6x) is 2(-1/6 xcos(6x)+1/36 sin(6x))+C

Popular >

integral of 2xsin(6x)

\int 2 x sin (6 x) d x

2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x)) + C

Solution steps

\int 2 x sin (6 x) d x

Take the constant out:

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

= 2 \cdot \int x sin (6 x) d x

Apply Integration By Parts

= 2 (- \frac{1}{6} x cos (6 x) - \int - \frac{1}{6} cos (6 x) d x)

\int - \frac{1}{6} cos (6 x) d x = - \frac{1}{36} sin (6 x)

= 2 (- \frac{1}{6} x cos (6 x) - (- \frac{1}{36} sin (6 x)))

Simplify

= 2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x))

Add a constant to the solution

= 2 (- \frac{1}{6} x cos (6 x) + \frac{1}{36} sin (6 x)) + C

\int (sin^{2} (\frac{x}{2})) d x

\int \frac{x ^{4}}{( 1 - x ^{2} ) ^{3}} d x

\int \frac{s}{3 - 2 s - s ^{2}} d s

\int \frac{x ^{3} ln ( x )}{2} d x

\int (x^{5} - x^{3} + x) e^{- x} d x

What is the integral of 2xsin(6x) ?
The integral of 2xsin(6x) is 2(-1/6 xcos(6x)+1/36 sin(6x))+C