What is the integral of tsin(t)cos(2t) ?

The integral of tsin(t)cos(2t) is 1/2 t(-1/3 cos(3t)+cos(t))-1/2 (-1/9 sin(3t)+sin(t))+C

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integral of tsin(t)cos(2t)

\int t sin (t) cos (2 t) d t

\frac{1}{2} t (- \frac{1}{3} cos (3 t) + cos (t)) - \frac{1}{2} (- \frac{1}{9} sin (3 t) + sin (t)) + C

Solution steps

\int t sin (t) cos (2 t) d t

Apply Integration By Parts

: \frac{1}{2} t (- \frac{1}{3} cos (3 t) + cos (t)) - \int \frac{1}{2} (- \frac{1}{3} cos (3 t) + cos (t)) d t

= \frac{1}{2} t (- \frac{1}{3} cos (3 t) + cos (t)) - \int \frac{1}{2} (- \frac{1}{3} cos (3 t) + cos (t)) d t

\int \frac{1}{2} (- \frac{1}{3} cos (3 t) + cos (t)) d t = \frac{1}{2} (- \frac{1}{9} sin (3 t) + sin (t))

= \frac{1}{2} t (- \frac{1}{3} cos (3 t) + cos (t)) - \frac{1}{2} (- \frac{1}{9} sin (3 t) + sin (t))

Add a constant to the solution

= \frac{1}{2} t (- \frac{1}{3} cos (3 t) + cos (t)) - \frac{1}{2} (- \frac{1}{9} sin (3 t) + sin (t)) + C

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What is the integral of tsin(t)cos(2t) ?
The integral of tsin(t)cos(2t) is 1/2 t(-1/3 cos(3t)+cos(t))-1/2 (-1/9 sin(3t)+sin(t))+C