What is the integral of (x-6)sin(pix) ?

The integral of (x-6)sin(pix) is -1/pi cos(pix)(x-6)+1/(pi^2)sin(pix)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x-6)sin(pix)

\int (x - 6) sin (π x) d x

- \frac{1}{π} cos (π x) (x - 6) + \frac{1}{π ^{2}} sin (π x) + C

Solution steps

\int (x - 6) sin (π x) d x

Apply Integration By Parts

: - \frac{1}{π} cos (π x) (x - 6) - \int - \frac{1}{π} cos (π x) d x

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

\int - \frac{1}{π} cos (π x) d x = - \frac{1}{π ^{2}} sin (π x)

= - \frac{1}{π} cos (π x) (x - 6) - (- \frac{1}{π ^{2}} sin (π x))

Simplify

= - \frac{1}{π} cos (π x) (x - 6) + \frac{1}{π ^{2}} sin (π x)

Add a constant to the solution

= - \frac{1}{π} cos (π x) (x - 6) + \frac{1}{π ^{2}} sin (π x) + C

cos^{3} (t)

\frac{d}{d x} (\frac{- 3}{x ^{4}})

\int_{0}^{π} 4 cos^{4} (x) sin (x) d x

18 e^{x} + 15 x

\frac{d}{d x} (3 e^{x + 1})

What is the integral of (x-6)sin(pix) ?
The integral of (x-6)sin(pix) is -1/pi cos(pix)(x-6)+1/(pi^2)sin(pix)+C