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Popular >

integral of (x^2)/y

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= \frac{1}{y} \cdot \int x^{2} d x

Apply the Power Rule

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

= \frac{1}{y} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{y} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 y}

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

Add a constant to the solution

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

Popular Examples

(dy)/(dx)=(3ex-9e-x)^2

\frac{d y}{d x} = (3 e x - 9 e - x)^{2}

integral from 1 to 2 of 7/(x^2)

\int_{1}^{2} \frac{7}{x ^{2}} d x

(dy)/(dx)=3x^{-2}e^{-y}

\frac{d y}{d x} = 3 x^{- 2} e^{- y}

integral of ((x^2+9x+1))/((x^2+1)^2)

\int \frac{( x ^{2} + 9 x + 1 )}{( x ^{2} + 1 ) ^{2}} d x

x^2y^{''}+4xy^'-4y=0,y(1)=0,y^'(1)=3

x^{2} y^{^{''}} + 4 x y^{^{'}} - 4 y = 0, y (1) = 0, y^{^{'}} (1) = 3

Frequently Asked Questions (FAQ)

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