What is the integral of 7x^2sin(2x) ?

The integral of 7x^2sin(2x) is 7(-1/2 x^2cos(2x)+1/4 (2xsin(2x)+cos(2x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7x^2sin(2x)

\int 7 x^{2} sin (2 x) d x

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

Solution steps

\int 7 x^{2} sin (2 x) d x

Take the constant out:

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

= 7 \cdot \int x^{2} sin (2 x) d x

Apply Integration By Parts

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

= 7 (- \frac{1}{2} x^{2} cos (2 x) - \int - x cos (2 x) d x)

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

= 7 (- \frac{1}{2} x^{2} cos (2 x) - (- \frac{1}{4} (2 x sin (2 x) + cos (2 x))))

Simplify

= 7 (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x)))

Add a constant to the solution

= 7 (- \frac{1}{2} x^{2} cos (2 x) + \frac{1}{4} (2 x sin (2 x) + cos (2 x))) + C

k = 1 \sum \infty (\frac{1}{2})^{k}

\frac{d}{d x} (\frac{x ^{2}}{64} + \frac{y ^{2}}{25}) = 1

x \to 2 - lim (\frac{- 1}{x ^{2} - 4})

\int \frac{14 x - 1}{( 4 x + 1 ) ( x - 2 )} d x

\int 2 x cos (- 4 x) d x

What is the integral of 7x^2sin(2x) ?
The integral of 7x^2sin(2x) is 7(-1/2 x^2cos(2x)+1/4 (2xsin(2x)+cos(2x)))+C