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Popular Calculus >

integral of (3s+4)^2

Solution

\int (3 s + 4)^{2} d s

Solution

3 s^{3} + 12 s^{2} + 16 s + C

Solution steps

\int (3 s + 4)^{2} d s

Expand

(3 s + 4)^{2} : 9 s^{2} + 24 s + 16

= \int 9 s^{2} + 24 s + 16 d s

Apply the Sum Rule:

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

= \int 9 s^{2} d s + \int 24 s d s + \int 16 d s

\int 9 s^{2} d s = 3 s^{3}

\int 24 s d s = 12 s^{2}

\int 16 d s = 16 s

= 3 s^{3} + 12 s^{2} + 16 s

Add a constant to the solution

= 3 s^{3} + 12 s^{2} + 16 s + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (3s+4)^2 ?
The integral of (3s+4)^2 is 3s^3+12s^2+16s+C