What is the integral of tcos^2(t) ?

The integral of tcos^2(t) is 1/2 t(t+1/2 sin(2t))-1/2 ((t^2)/2-1/4 cos(2t))+C

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integral of tcos^2(t)

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

\frac{1}{2} t (t + \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} - \frac{1}{4} cos (2 t)) + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{1}{2} (t + \frac{1}{2} sin (2 t)) d t = \frac{1}{2} (\frac{t ^{2}}{2} - \frac{1}{4} cos (2 t))

= \frac{1}{2} t (t + \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} - \frac{1}{4} cos (2 t))

Add a constant to the solution

= \frac{1}{2} t (t + \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} - \frac{1}{4} cos (2 t)) + C

ln (2)

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

\frac{d x}{d t} = t x^{\frac{1}{3}}

\int_{0}^{1} (x - 3) e^{x} d x

f (x) = 8 x^{5} - 8 cos (x)

What is the integral of tcos^2(t) ?
The integral of tcos^2(t) is 1/2 t(t+1/2 sin(2t))-1/2 ((t^2)/2-1/4 cos(2t))+C