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Popular >

integral of (5x)^2

Solution

\int (5 x)^{2} d x

Solution

\frac{25 x ^{3}}{3} + C

Solution steps

\int (5 x)^{2} d x

Simplify

(5 x)^{2} : 25 x^{2}

= \int 25 x^{2} d x

Take the constant out:

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

= 25 \cdot \int x^{2} d x

Apply the Power Rule

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

= 25 \cdot \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{25 x ^{3}}{3}

Add a constant to the solution

= \frac{25 x ^{3}}{3} + C

Graph

Popular Examples

integral of (2-x)^{5/2}

\int (2 - x)^{\frac{5}{2}} d x

integral of sec^2(9x)tan^2(9x)

\int sec^{2} (9 x) tan^{2} (9 x) d x

integral of 1/(sin^6(x))

\int \frac{1}{sin ^{6} ( x )} d x

integral of x(5x-1)^{15}

\int x (5 x - 1)^{15} d x

integral of (3x+1)/(x^2-x-2)

\int \frac{3 x + 1}{x ^{2} - x - 2} d x

Frequently Asked Questions (FAQ)

What is the integral of (5x)^2 ?
The integral of (5x)^2 is (25x^3)/3+C