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Popular >

integral of y(x+y)

Solution

\int y (x + y) d y

Solution

\frac{x y ^{2}}{2} + \frac{y ^{3}}{3} + C

Solution steps

\int y (x + y) d y

Expand

(x + y) y : x y + y^{2}

= \int x y + y^{2} 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 x y d y + \int y^{2} d y

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

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

= \frac{x y ^{2}}{2} + \frac{y ^{3}}{3}

Add a constant to the solution

= \frac{x y ^{2}}{2} + \frac{y ^{3}}{3} + C

Graph

Popular Examples

integral of 1/((121-x^2)^{3/2)}

\int \frac{1}{( 121 - x ^{2} ) ^{\frac{3}{2}}} d x

limit as x approaches 0+of x^{8/x}

x \to 0 + lim (x^{\frac{8}{x}})

derivative of x^2sin(8x)derivative of

x^{2} sin (8 x)

y^{^{''}} - 4 y = 0

integral of (x^{3/2}+6)^8sqrt(x)

\int (x^{\frac{3}{2}} + 6)^{8} x d x

Frequently Asked Questions (FAQ)

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