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Popular Calculus >

integral of x(18x+6)

Solution

\int x (18 x + 6) d x

Solution

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

Solution steps

\int x (18 x + 6) d x

Expand

x (18 x + 6) : 18 x^{2} + 6 x

= \int 18 x^{2} + 6 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 18 x^{2} d x + \int 6 x d x

\int 18 x^{2} d x = 6 x^{3}

\int 6 x d x = 3 x^{2}

= 6 x^{3} + 3 x^{2}

Add a constant to the solution

= 6 x^{3} + 3 x^{2} + C

Graph

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\frac{d}{d x} (2 x - \frac{4}{x})

integral of (x^2)/(sqrt(81+x^2))

\int \frac{x ^{2}}{81 + x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of x(18x+6) ?
The integral of x(18x+6) is 6x^3+3x^2+C