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Popular >

integral of xy^3

Solution

\int x y^{3} d x

Solution

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

Solution steps

\int x 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 d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of x^3tan^3(x^4)

\int x^{3} tan^{3} (x^{4}) d x

f (x) = 3 x

y^'+1/(x+8)y=x^{-2},y(1)=5

y^{^{'}} + \frac{1}{x + 8} y = x^{- 2}, y (1) = 5

derivative of ((x+1^3)/(x^{3/2)})

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}})

inverse oflaplace (5+5s)/((s^2+25)^2)inverse laplace

\frac{5 + 5 s}{( s ^{2} + 25 ) ^{2}}

Frequently Asked Questions (FAQ)

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