What is the integral of x^3sin(4x) ?

The integral of x^3sin(4x) is -1/4 x^3cos(4x)+3/128 (8x^2sin(4x)+4xcos(4x)-sin(4x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3sin(4x)

\int x^{3} sin (4 x) d x

- \frac{1}{4} x^{3} cos (4 x) + \frac{3}{128} (8 x^{2} sin (4 x) + 4 x cos (4 x) - sin (4 x)) + C

Solution steps

\int x^{3} sin (4 x) d x

Apply Integration By Parts

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

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

\int - \frac{3}{4} x^{2} cos (4 x) d x = - \frac{3}{128} (8 x^{2} sin (4 x) + 4 x cos (4 x) - sin (4 x))

= - \frac{1}{4} x^{3} cos (4 x) - (- \frac{3}{128} (8 x^{2} sin (4 x) + 4 x cos (4 x) - sin (4 x)))

Simplify

= - \frac{1}{4} x^{3} cos (4 x) + \frac{3}{128} (8 x^{2} sin (4 x) + 4 x cos (4 x) - sin (4 x))

Add a constant to the solution

= - \frac{1}{4} x^{3} cos (4 x) + \frac{3}{128} (8 x^{2} sin (4 x) + 4 x cos (4 x) - sin (4 x)) + C

\frac{5 x ^{4} - 3 x ^{3}}{x ^{5}}

\int_{0}^{1} \frac{4 - x}{1 + x ^{2}} d x

\int \frac{sec ^{2} ( 8 x )}{tan ( 8 x ) + 5} d x

\frac{\partial}{\partial x} (1 (x - y) e^{1 y + 5 x^{2}})

\frac{\partial}{\partial x} (x cos (\frac{x}{y}))

What is the integral of x^3sin(4x) ?
The integral of x^3sin(4x) is -1/4 x^3cos(4x)+3/128 (8x^2sin(4x)+4xcos(4x)-sin(4x))+C