What is the integral of t*cos(t) ?

The integral of t*cos(t) is tsin(t)+cos(t)+C

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integral of t*cos(t)

\int t \cdot cos (t) d t

t sin (t) + cos (t) + C

Solution steps

\int t cos (t) d t

Apply Integration By Parts

: t sin (t) - \int sin (t) d t

= t sin (t) - \int sin (t) d t

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

= t sin (t) - (- cos (t))

Simplify

= t sin (t) + cos (t)

Add a constant to the solution

= t sin (t) + cos (t) + C

\int 18 sin^{3} (x) cos^{2} (x) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + e^{- x}

t e^{2 t} sin (6 t)

\frac{d}{d x} (e^{x} cos (x) - x^{3} sin (x) + π)

y^{^{'}} = \frac{y}{50} 5, y (0) = 30