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

The integral of x^3cos(4x) is 1/4 x^3sin(4x)-3/4 (-1/4 x^2cos(4x)+1/32 (4xsin(4x)+cos(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^3cos(4x)

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

\frac{1}{4} x^{3} sin (4 x) - \frac{3}{4} (- \frac{1}{4} x^{2} cos (4 x) + \frac{1}{32} (4 x sin (4 x) + cos (4 x))) + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{3}{4} x^{2} sin (4 x) d x = \frac{3}{4} (- \frac{1}{4} x^{2} cos (4 x) + \frac{1}{32} (4 x sin (4 x) + cos (4 x)))

= \frac{1}{4} x^{3} sin (4 x) - \frac{3}{4} (- \frac{1}{4} x^{2} cos (4 x) + \frac{1}{32} (4 x sin (4 x) + cos (4 x)))

Add a constant to the solution

= \frac{1}{4} x^{3} sin (4 x) - \frac{3}{4} (- \frac{1}{4} x^{2} cos (4 x) + \frac{1}{32} (4 x sin (4 x) + cos (4 x))) + C

a

(y^{2} + 8) d x = y sec^{2} (x) d y

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

x \to 1 lim (e^{3 x^{5} - 3 x})

f (x) = \frac{5}{x}

What is the integral of x^3cos(4x) ?
The integral of x^3cos(4x) is 1/4 x^3sin(4x)-3/4 (-1/4 x^2cos(4x)+1/32 (4xsin(4x)+cos(4x)))+C