What is the integral of t^2sin(Bt) ?

The integral of t^2sin(Bt) is -1/B t^2cos(Bt)+2/(B^3)(Btsin(Bt)+cos(Bt))+C

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integral of t^2sin(Bt)

\int t^{2} sin (Bt) d t

- \frac{1}{B} t^{2} cos (Bt) + \frac{2}{B ^{3}} (Bt sin (Bt) + cos (Bt)) + C

Solution steps

\int t^{2} sin (Bt) d t

Apply Integration By Parts

: - \frac{1}{B} t^{2} cos (Bt) - \int - \frac{2}{B} t cos (Bt) d t

= - \frac{1}{B} t^{2} cos (Bt) - \int - \frac{2}{B} t cos (Bt) d t

\int - \frac{2}{B} t cos (Bt) d t = - \frac{2}{B ^{3}} (Bt sin (Bt) + cos (Bt))

= - \frac{1}{B} t^{2} cos (Bt) - (- \frac{2}{B ^{3}} (Bt sin (Bt) + cos (Bt)))

Simplify

= - \frac{1}{B} t^{2} cos (Bt) + \frac{2}{B ^{3}} (Bt sin (Bt) + cos (Bt))

Add a constant to the solution

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

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What is the integral of t^2sin(Bt) ?
The integral of t^2sin(Bt) is -1/B t^2cos(Bt)+2/(B^3)(Btsin(Bt)+cos(Bt))+C