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Popular Calculus >

integral of (1+2y)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

Apply the Sum Rule:

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

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

\int 1 d y = y

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

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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