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Popular >

integral of xg(x^2)

Solution

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

Solution

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

Solution steps

\int xg x^{2} d x

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(sqrt(5x+1))

\int \frac{1}{5 x + 1} d x

integral of (8x^2-5x+1)/(x^2+x)

\int \frac{8 x ^{2} - 5 x + 1}{x ^{2} + x} d x

derivative of 6cos(x+6xsin(x))

\frac{d}{d x} (6 cos (x) + 6 x sin (x))

limit as x approaches 4 of sqrt(4)+2

x \to 4 lim (4 + 2)

integral from-1 to 3 of 1

\int_{- 1}^{3} 1 d x

Frequently Asked Questions (FAQ)

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