What is the integral of x*cos(pix) ?

The integral of x*cos(pix) is 1/pi xsin(pix)+1/(pi^2)cos(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*cos(pix)

\int x \cdot cos (π x) d x

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

Solution steps

\int x cos (π x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int (- 7 x + 5)^{3} d x

\int \frac{( 2 x + 1 ) ^{2}}{x} d x

\int (1 + t) e^{t} d t

\int cot (x) csc^{4} (x) d x

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

What is the integral of x*cos(pix) ?
The integral of x*cos(pix) is 1/pi xsin(pix)+1/(pi^2)cos(pix)+C