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Popular >

integral of (xy^2)

Solution

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

Solution

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

Solution steps

\int x y^{2} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of sin(10pi)t

\int sin (10 π) t d t

integral of 9x^3e^{x^4}

\int 9 x^{3} e^{x^{4}} d x

integral of 5/((2x-1)^2)

\int \frac{5}{( 2 x - 1 ) ^{2}} d x

integral of ((e^x+e^{-x})/2)^2

\int (\frac{e ^{x} + e ^{- x}}{2})^{2} d x

integral of e^5x

\int e^{5} x d x

Frequently Asked Questions (FAQ)

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