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Popular >

integral of (3x^2)^2

Solution

\int (3 x^{2})^{2} d x

Solution

\frac{9 x ^{5}}{5} + C

Solution steps

\int (3 x^{2})^{2} d x

Simplify

(3 x^{2})^{2} : 9 x^{4}

= \int 9 x^{4} d x

Take the constant out:

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

= 9 \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= 9 \cdot \frac{x ^{5}}{5}

Multiply fractions:

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

= \frac{9 x ^{5}}{5}

Add a constant to the solution

= \frac{9 x ^{5}}{5} + C

Popular Examples

integral of 2sec^2(θ)tan(θ)

\int 2 sec^{2} (θ) tan (θ) d θ

integral of (x^3)/(3x^4-5)

\int \frac{x ^{3}}{3 x ^{4} - 5} d x

integral of (2x^3+9x^2+14x+8)/((x^2+2x)(x^2+2))

\int \frac{2 x ^{3} + 9 x ^{2} + 14 x + 8}{( x ^{2} + 2 x ) ( x ^{2} + 2 )} d x

integral of 1/(x+1)integral

\frac{1}{x + 1}

integral of (6e^x-x^3(sqrt(x)+1))

\int (6 e^{x} - x^{3} (x + 1)) d x

Frequently Asked Questions (FAQ)

What is the integral of (3x^2)^2 ?
The integral of (3x^2)^2 is (9x^5)/5+C