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Popular >

integral of x^3+y^3

Solution

\int x^{3} + y^{3} d x

Solution

y^{3} x + \frac{x ^{4}}{4} + C

Solution steps

\int x^{3} + y^{3} 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^{3} d x + \int x^{3} d x

\int y^{3} d x = y^{3} x

\int x^{3} d x = \frac{x ^{4}}{4}

= y^{3} x + \frac{x ^{4}}{4}

Add a constant to the solution

= y^{3} x + \frac{x ^{4}}{4} + C

Popular Examples

integral of (xsin^2(x))/2

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

integral of (8+4x)/(49+64x^2)

\int \frac{8 + 4 x}{49 + 64 x ^{2}} d x

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

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

integral of sin(6x)sin(8x)

\int sin (6 x) sin (8 x) d x

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

\int \frac{2}{x ^{2} - 2 x + 1} d x

Frequently Asked Questions (FAQ)

What is the integral of x^3+y^3 ?
The integral of x^3+y^3 is y^3x+(x^4)/4+C