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Popular >

integral of (x+y)^2

Solution

integral

(x + y)^{2}

Solution

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

Solution steps

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

Expand

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

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (k*x)/((1+x^2))integral

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\frac{x ^{2}}{( 1 - x ^{2} )}

integral of x/((1+x^2))integral

\frac{x}{( 1 + x ^{2} )}

Frequently Asked Questions (FAQ)

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