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Popular >

integral of x^2n^2x

Solution

\int x^{2} n^{2} x d x

Solution

\frac{n ^{2} x ^{4}}{4} + C

Solution steps

\int x^{2} n^{2} x d x

Take the constant out:

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

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

Simplify

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

= n^{2} \cdot \int x^{3} d x

Apply the Power Rule

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

= n^{2} \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{n ^{2} x ^{4}}{4}

Add a constant to the solution

= \frac{n ^{2} x ^{4}}{4} + C

Popular Examples

integral from 0 to 1 of (t^2)/(1+t^6)

\int_{0}^{1} \frac{t ^{2}}{1 + t ^{6}} d t

derivative of (sqrt(x))/(x+3)derivative of

\frac{x}{x + 3}

tangent of (2x-1)^{(2)}ln(2x-1)tangent of

(2 x - 1)^{(2)} ln (2 x - 1)

derivative of arctan(sqrt(x^2-2)+C)

\frac{d}{d x} (arctan (x^{2} - 2) + C)

integral of (sec^2(x))/((1+tan(x))^2)

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

Frequently Asked Questions (FAQ)

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