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Popular Calculus >

integral of (2u+1)^2

Solution

\int (2 u + 1)^{2} d u

Solution

\frac{4 u ^{3}}{3} + 2 u^{2} + u + C

Solution steps

\int (2 u + 1)^{2} d u

Expand

(2 u + 1)^{2} : 4 u^{2} + 4 u + 1

= \int 4 u^{2} + 4 u + 1 d u

Apply the Sum Rule:

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

= \int 4 u^{2} d u + \int 4 u d u + \int 1 d u

\int 4 u^{2} d u = \frac{4 u ^{3}}{3}

\int 4 u d u = 2 u^{2}

\int 1 d u = u

= \frac{4 u ^{3}}{3} + 2 u^{2} + u

Add a constant to the solution

= \frac{4 u ^{3}}{3} + 2 u^{2} + u + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (2u+1)^2 ?
The integral of (2u+1)^2 is (4u^3)/3+2u^2+u+C