What is the integral of tsin(6t) ?

The integral of tsin(6t) is -1/6 tcos(6t)+1/36 sin(6t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of tsin(6t)

\int t sin (6 t) d t

- \frac{1}{6} t cos (6 t) + \frac{1}{36} sin (6 t) + C

Solution steps

\int t sin (6 t) d t

Apply Integration By Parts

= - \frac{1}{6} t cos (6 t) - \int - \frac{1}{6} cos (6 t) d t

\int - \frac{1}{6} cos (6 t) d t = - \frac{1}{36} sin (6 t)

= - \frac{1}{6} t cos (6 t) - (- \frac{1}{36} sin (6 t))

Simplify

= - \frac{1}{6} t cos (6 t) + \frac{1}{36} sin (6 t)

Add a constant to the solution

= - \frac{1}{6} t cos (6 t) + \frac{1}{36} sin (6 t) + C

\int 16 x^{2} + 1 d x

\int (4 x^{3} + \frac{375}{8 x ^{4}}) d x

\int sec (12 x) tan (12 x) d x

\int - x cos (3 x) d x

\int (x + 1)^{2} \cdot 3^{- x} d x

What is the integral of tsin(6t) ?
The integral of tsin(6t) is -1/6 tcos(6t)+1/36 sin(6t)+C