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Popular >

integral of x(12x+8)

Solution

\int x (12 x + 8) d x

Solution

4 x^{3} + 4 x^{2} + C

Solution steps

\int x (12 x + 8) d x

Expand

x (12 x + 8) : 12 x^{2} + 8 x

= \int 12 x^{2} + 8 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

= \int 12 x^{2} d x + \int 8 x d x

\int 12 x^{2} d x = 4 x^{3}

\int 8 x d x = 4 x^{2}

= 4 x^{3} + 4 x^{2}

Add a constant to the solution

= 4 x^{3} + 4 x^{2} + C

Popular Examples

limit as x approaches 0 of e^{-1/x}

x \to 0 lim (e^{- \frac{1}{x}})

(dy)/(dx)=(2xy)/(x^2+y^2)

\frac{d y}{d x} = \frac{2 x y}{x ^{2} + y ^{2}}

integral of (-9x^2+9x+2)

\int (- 9 x^{2} + 9 x + 2) d x

derivative of y=(x^3+8x^2)^{-1}derivative of

y = (x^{3} + 8 x^{2})^{- 1}

derivative of f(x)=(2x+5)/(x-1)derivative of

f (x) = \frac{2 x + 5}{x - 1}

Frequently Asked Questions (FAQ)

What is the integral of x(12x+8) ?
The integral of x(12x+8) is 4x^3+4x^2+C