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Popular >

integral of (3m+4)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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 m^{2} d m + \int 24 m d m + \int 16 d m

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

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

\int 16 d m = 16 m

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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