What is the integral of 3xsin(5x) ?

The integral of 3xsin(5x) is 3(-1/5 xcos(5x)+1/25 sin(5x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3xsin(5x)

\int 3 x sin (5 x) d x

3 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x)) + C

Solution steps

\int 3 x sin (5 x) d x

Take the constant out:

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

= 3 \cdot \int x sin (5 x) d x

Apply Integration By Parts

: - \frac{1}{5} x cos (5 x) - \int - \frac{1}{5} cos (5 x) d x

= 3 (- \frac{1}{5} x cos (5 x) - \int - \frac{1}{5} cos (5 x) d x)

\int - \frac{1}{5} cos (5 x) d x = - \frac{1}{25} sin (5 x)

= 3 (- \frac{1}{5} x cos (5 x) - (- \frac{1}{25} sin (5 x)))

Simplify

= 3 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x))

Add a constant to the solution

= 3 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x)) + C

x = 9 y^{2}, x = 28 + 2 y^{2}

\int - e^{t} d t

f (x) = 3 - 6 x^{2}, - 57, at x = 3

x \to 3 - lim (ln (x - 3))

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

What is the integral of 3xsin(5x) ?
The integral of 3xsin(5x) is 3(-1/5 xcos(5x)+1/25 sin(5x))+C