What is the integral of 3t^2sin(t) ?

The integral of 3t^2sin(t) is 3(-t^2cos(t)+2(tsin(t)+cos(t)))+C

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integral of 3t^2sin(t)

\int 3 t^{2} sin (t) d t

3 (- t^{2} cos (t) + 2 (t sin (t) + cos (t))) + C

Solution steps

\int 3 t^{2} sin (t) d t

Take the constant out:

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

= 3 \cdot \int t^{2} sin (t) d t

Apply Integration By Parts

: - t^{2} cos (t) - \int - 2 t cos (t) d t

= 3 (- t^{2} cos (t) - \int - 2 t cos (t) d t)

\int - 2 t cos (t) d t = - 2 (t sin (t) + cos (t))

= 3 (- t^{2} cos (t) - (- 2 (t sin (t) + cos (t))))

Simplify

= 3 (- t^{2} cos (t) + 2 (t sin (t) + cos (t)))

Add a constant to the solution

= 3 (- t^{2} cos (t) + 2 (t sin (t) + cos (t))) + C

\frac{\partial}{\partial x} (\frac{1}{\frac{1}{x} + \frac{1}{o}})

\frac{\partial}{\partial y} (3 x^{\frac{y}{z}})

\frac{\partial}{\partial y} (2 e^{- 2 x y} + x y^{3})

x, 20 - x^{2}

x \to 2 lim (2 x - x^{2})

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