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

\frac{d}{d x} (3 x - \frac{11}{x ^{12}})

f (x) = 7 x - 6 x, (1, 1)

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = x

\frac{\partial}{\partial x} (e^{x} \cdot sin (x))

8 y^{^{'}} = 3 e^{\frac{x}{8}} + y

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