en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^xsin(y)-2ysin(x)

Solution

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

Solution

e^{x} sin (y) + 2 y cos (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 2 sin (x) y d x = - 2 y cos (x)

= sin (y) e^{x} - (- 2 y cos (x))

Simplify

= e^{x} sin (y) + 2 y cos (x)

Add a constant to the solution

= e^{x} sin (y) + 2 y cos (x) + C

Popular Examples

integral of (e^{2x})/(sqrt(e^{2x)+1)}

\int \frac{e ^{2 x}}{e ^{2 x} + 1} d x

integral of (3tan(x))/(cos(x))

\int \frac{3 tan ( x )}{cos ( x )} d x

integral of y/(3y^2+1)

\int \frac{y}{3 y ^{2} + 1} d y

integral of 6/(7+y^2)

\int \frac{6}{7 + y ^{2}} d y

integral of y/(x(2-x^2))

\int \frac{y}{x ( 2 - x ^{2} )} d x

Frequently Asked Questions (FAQ)

What is the integral of e^xsin(y)-2ysin(x) ?
The integral of e^xsin(y)-2ysin(x) is e^xsin(y)+2ycos(x)+C