What is the integral of 27xsin(3x) ?

The integral of 27xsin(3x) is 27(-1/3 xcos(3x)+1/9 sin(3x))+C

Popular >

integral of 27xsin(3x)

\int 27 x sin (3 x) d x

27 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

Solution steps

\int 27 x sin (3 x) d x

Take the constant out:

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

= 27 \cdot \int x sin (3 x) d x

Apply Integration By Parts

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

= 27 (- \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x)

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= 27 (- \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x)))

Simplify

= 27 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x))

Add a constant to the solution

= 27 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

\int \frac{cos ( y )}{sin ( y ) - 1} d y

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

\int \frac{1}{x + 10} d x

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

\int 2^{x l n (x)} (1 + ln (x)) d x

What is the integral of 27xsin(3x) ?
The integral of 27xsin(3x) is 27(-1/3 xcos(3x)+1/9 sin(3x))+C