What is the integral of 2xsin(x)e^x ?

The integral of 2xsin(x)e^x is -e^xxcos(x)+e^xxsin(x)+e^xcos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2xsin(x)e^x

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

- e^{x} x cos (x) + e^{x} x sin (x) + e^{x} cos (x) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

2 (x (- \frac{1}{2} e^{x} cos (x) + \frac{1}{2} e^{x} sin (x)) - (- \frac{1}{2} e^{x} cos (x))) : - e^{x} x cos (x) + e^{x} x sin (x) + e^{x} cos (x)

= - e^{x} x cos (x) + e^{x} x sin (x) + e^{x} cos (x)

Add a constant to the solution

= - e^{x} x cos (x) + e^{x} x sin (x) + e^{x} cos (x) + C

\frac{e ^{- 4 s}}{2 s - 1}

x^{2} sin (x)

x \to \frac{1}{5} + lim (\frac{x}{10 x - 2})

\int \frac{2 x}{3 x + 1} d x

What is the integral of 2xsin(x)e^x ?
The integral of 2xsin(x)e^x is -e^xxcos(x)+e^xxsin(x)+e^xcos(x)+C