What is the integral of y^2+ysin(x) ?

The integral of y^2+ysin(x) is (y^3)/3+1/2 y^2sin(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of y^2+ysin(x)

\int y^{2} + y sin (x)

\frac{y ^{3}}{3} + \frac{1}{2} y^{2} sin (x) + C

Solution steps

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

Apply the Sum Rule:

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

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

\int y^{2} d y = \frac{y ^{3}}{3}

\int sin (x) y d y = \frac{1}{2} y^{2} sin (x)

= \frac{y ^{3}}{3} + \frac{1}{2} y^{2} sin (x)

Add a constant to the solution

= \frac{y ^{3}}{3} + \frac{1}{2} y^{2} sin (x) + C

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

f (x) = x sin (x)

y^{^{'}} = e^{3 x + 2 y}

e^{2 x - 3}

\frac{\partial}{\partial x} (\frac{1}{3 x ^{2} + y})

What is the integral of y^2+ysin(x) ?
The integral of y^2+ysin(x) is (y^3)/3+1/2 y^2sin(x)+C