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

The integral of-2tcos(t) is -2(tsin(t)+cos(t))+C

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integral of-2tcos(t)

\int - 2 t cos (t) d t

- 2 (t sin (t) + cos (t)) + C

Solution steps

\int - 2 t cos (t) d t

Take the constant out:

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

= - 2 \cdot \int t cos (t) d t

Apply Integration By Parts

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

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

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

= - 2 (t sin (t) - (- cos (t)))

Simplify

= - 2 (t sin (t) + cos (t))

Add a constant to the solution

= - 2 (t sin (t) + cos (t)) + C

\int 48 t^{7} e^{- t^{8}} d t

\int x (3 x + 10)^{49} d x

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

\frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{x ^{3}}

x^{2} y \frac{d y}{d x} - 9 = 0

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