What is the integral of tsin(t/2) ?

The integral of tsin(t/2) is -2tcos(t/2)+4sin(t/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tsin(t/2)

\int t sin (\frac{t}{2}) d t

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

Solution steps

\int t sin (\frac{t}{2}) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{x + 5}{x ^{2} + 4} d x

\int_{0}^{1} \frac{1}{x ^{2} - 1} d x

\int \frac{e ^{- x}}{1} d x

(- 8, - 3), (- 12, - 3)

\frac{\partial}{\partial x} (7 x - y)

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