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Popular >

integral of x^3+x^2y

Solution

\int x^{3} + x^{2} y d y

Solution

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

Solution steps

\int x^{3} + x^{2} y 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^{3} d y + \int x^{2} y d y

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

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

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

Add a constant to the solution

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

Popular Examples

integral of sqrt((x^2)/4+(3x)/4+2)

\int \frac{x ^{2}}{4} + \frac{3 x}{4} + 2 d x

integral of x^3log_{e}(x)

\int x^{3} lo g_{e} (x) d x

integral of 2x^2e^{3x+1}

\int 2 x^{2} e^{3 x + 1} d x

integral of ((x+1)e^{8x^2+16x})

\int ((x + 1) e^{8 x^{2} + 16 x}) d x

integral of 2^{x^2+1}*x

\int 2^{x^{2} + 1} \cdot x d x

Frequently Asked Questions (FAQ)

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