What is the integral of 8xsin(5-4x) ?

The integral of 8xsin(5-4x) is 8(1/4 xcos(5-4x)+1/16 sin(5-4x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 8xsin(5-4x)

\int 8 x sin (5 - 4 x) d x

8 (\frac{1}{4} x cos (5 - 4 x) + \frac{1}{16} sin (5 - 4 x)) + C

Solution steps

\int 8 x sin (5 - 4 x) d x

Take the constant out:

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

= 8 \cdot \int x sin (5 - 4 x) d x

Apply Integration By Parts

= 8 (\frac{1}{4} x cos (5 - 4 x) - \int \frac{1}{4} cos (5 - 4 x) d x)

\int \frac{1}{4} cos (5 - 4 x) d x = - \frac{1}{16} sin (5 - 4 x)

= 8 (\frac{1}{4} x cos (5 - 4 x) - (- \frac{1}{16} sin (5 - 4 x)))

Simplify

= 8 (\frac{1}{4} x cos (5 - 4 x) + \frac{1}{16} sin (5 - 4 x))

Add a constant to the solution

= 8 (\frac{1}{4} x cos (5 - 4 x) + \frac{1}{16} sin (5 - 4 x)) + C

\int 3 (x + 4)^{2} d x

in t e g r a l x^{2} ln (x)

\int x^{2} cos (1 - \frac{1}{4} x^{3}) d x

\int 3 z e^{- 3 yz} d y

\int \frac{1}{4 y - 1} d y

What is the integral of 8xsin(5-4x) ?
The integral of 8xsin(5-4x) is 8(1/4 xcos(5-4x)+1/16 sin(5-4x))+C