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Popular >

integral of x^2y^3

Solution

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

Solution

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= y^{3} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of nx^{n-1}

n = 1 \sum \infty n x^{n - 1}

integral of 3x^2e^{5x^3}

\int 3 x^{2} e^{5 x^{3}} d x

sum from n=1 to infinity of (ln(9n))/n

n = 1 \sum \infty \frac{ln ( 9 n )}{n}

derivative of ln(1+9x)

\frac{d}{d x} (ln (1 + 9 x))

e^{-x}y(dy)/(dx)=e^{-y}+e^{-2x-y}

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

Frequently Asked Questions (FAQ)

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