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Popular >

integral of (6x+3)^2

Solution

\int (6 x + 3)^{2} d x

Solution

12 x^{3} + 18 x^{2} + 9 x + C

Solution steps

\int (6 x + 3)^{2} d x

Expand

(6 x + 3)^{2} : 36 x^{2} + 36 x + 9

= \int 36 x^{2} + 36 x + 9 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 36 x^{2} d x + \int 36 x d x + \int 9 d x

\int 36 x^{2} d x = 12 x^{3}

\int 36 x d x = 18 x^{2}

\int 9 d x = 9 x

= 12 x^{3} + 18 x^{2} + 9 x

Add a constant to the solution

= 12 x^{3} + 18 x^{2} + 9 x + C

Graph

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\int (sec (x))^{2} (1 + tan (x)) d x

integral of 8sin(4y)

\int 8 sin (4 y) d y

Frequently Asked Questions (FAQ)

What is the integral of (6x+3)^2 ?
The integral of (6x+3)^2 is 12x^3+18x^2+9x+C