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Popular >

integral of (y+y^2)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (2x)/(x-3)

\int \frac{2 x}{x - 3} d x

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\int \frac{2 e ^{a r c c o s (x)}}{1 - x ^{2}} d x

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\int x (2 x + 3)^{5} d x

integral of sec(1/2)x

\int sec (\frac{1}{2}) x d x

integral of (ln(x))/(xsqrt(16-ln(x)))

\int \frac{ln ( x )}{x 16 - ln ( x )} d x

Frequently Asked Questions (FAQ)

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