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Popular >

integral of xf(x^2)

Solution

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

Solution

\frac{f x ^{4}}{4} + C

Solution steps

\int x f x^{2} d x

Take the constant out:

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

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

Simplify

x x^{2} : x^{3}

= f \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= f \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{f x ^{4}}{4}

Add a constant to the solution

= \frac{f x ^{4}}{4} + C

Popular Examples

integral of 1/(x(25-x))

\int \frac{1}{x ( 25 - x )} d x

integral of (sec(t))/(2sec^2(t)-1)

\int \frac{sec ( t )}{2 sec ^{2} ( t ) - 1} d t

integral of (x^2+5x+7)/(x^2+3x+4)

\int \frac{x ^{2} + 5 x + 7}{x ^{2} + 3 x + 4} d x

integral of (xsqrt(x)+\sqrt[4]{x})/(x^2)

integral of 2-x^2+x

\int 2 - x^{2} + x d x

Frequently Asked Questions (FAQ)

What is the integral of xf(x^2) ?
The integral of xf(x^2) is (fx^4)/4+C