What is the integral of xcos(bx) ?

The integral of xcos(bx) is 1/(b^2)(bxsin(bx)+cos(bx))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xcos(bx)

\int x cos (b x) d x

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

Solution steps

\int x cos (b x) d x

Apply u-substitution

: \int \frac{u cos ( u )}{b ^{2}} d u

= \int \frac{u cos ( u )}{b ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{b ^{2}} \cdot \int u cos (u) d u

Apply Integration By Parts

: u sin (u) - \int sin (u) d u

= \frac{1}{b ^{2}} (u sin (u) - \int sin (u) d u)

\int sin (u) d u = - cos (u)

= \frac{1}{b ^{2}} (u sin (u) - (- cos (u)))

Substitute back

u = b x

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

Simplify

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

Add a constant to the solution

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

\frac{d y}{d x}, y = \frac{6}{x}

(2 x + ln (y)) d x + (\frac{x}{y}) d y = 0

(3.11) (11.8)

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin (x) d x

4 x + y^{2} = 12, y = x

What is the integral of xcos(bx) ?
The integral of xcos(bx) is 1/(b^2)(bxsin(bx)+cos(bx))+C