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Popular >

integral of (2x)^2

Solution

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

Solution

\frac{4 x ^{3}}{3} + C

Solution steps

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

Simplify

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

= \int 4 x^{2} d x

Take the constant out:

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

= 4 \cdot \int x^{2} d x

Apply the Power Rule

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

= 4 \cdot \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{4 x ^{3}}{3}

Add a constant to the solution

= \frac{4 x ^{3}}{3} + C

Popular Examples

slope of (-2,-6),(2,2)slope

(- 2, - 6), (2, 2)

tangent of f(x)=9+4x^2-2x^3,\at x=1 tangent of

f (x) = 9 + 4 x^{2} - 2 x^{3}, at x = 1

derivative of y=ln(ln(x^3))derivative of

y = ln (ln (x^{3}))

derivative of y=(sin(x))/(1+sin(x))derivative of

y = \frac{sin ( x )}{1 + sin ( x )}

integral of x/(x^2+3)

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

Frequently Asked Questions (FAQ)

What is the integral of (2x)^2 ?
The integral of (2x)^2 is (4x^3)/3+C