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Popular >

integral of 3x(x+2)

Solution

\int 3 x (x + 2) d x

Solution

x^{3} + 3 x^{2} + C

Solution steps

\int 3 x (x + 2) d x

Take the constant out:

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

= 3 \cdot \int x (x + 2) d x

Expand

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= 3 (\frac{x ^{3}}{3} + x^{2})

Simplify

3 (\frac{x ^{3}}{3} + x^{2}) : x^{3} + 3 x^{2}

= x^{3} + 3 x^{2}

Add a constant to the solution

= x^{3} + 3 x^{2} + C

Popular Examples

integral of (7x+6)^{-2}

\int (7 x + 6)^{- 2} d x

integral of (x^3)/(sqrt(5-x^2))

\int \frac{x ^{3}}{5 - x ^{2}} d x

integral of (x-2)/(x-3)

\int \frac{x - 2}{x - 3} d x

integral of (12x^2)/(sqrt((4x^3+5)))

\int \frac{12 x ^{2}}{( 4 x ^{3} + 5 )} d x

integral of (x+1)sqrt(4-x)

\int (x + 1) 4 - x d x

Frequently Asked Questions (FAQ)

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