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Popular >

integral of x^2+y^2

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

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\int_{0}^{\infty} \frac{x}{1 + x ^{2}} d x

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\frac{d}{d x} (ln (tanh (\frac{x}{2})))

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\int 7 (1 + tan^{2} (x)) d x

Frequently Asked Questions (FAQ)

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