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Popular >

integral of (2y+3)^2

Solution

\int (2 y + 3)^{2} d y

Solution

\frac{4 y ^{3}}{3} + 6 y^{2} + 9 y + C

Solution steps

\int (2 y + 3)^{2} d y

Expand

(2 y + 3)^{2} : 4 y^{2} + 12 y + 9

= \int 4 y^{2} + 12 y + 9 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 4 y^{2} d y + \int 12 y d y + \int 9 d y

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

\int 12 y d y = 6 y^{2}

\int 9 d y = 9 y

= \frac{4 y ^{3}}{3} + 6 y^{2} + 9 y

Add a constant to the solution

= \frac{4 y ^{3}}{3} + 6 y^{2} + 9 y + C

Popular Examples

d/(dt)(e^{-3t})

\frac{d}{d t} (e^{- 3 t})

limit as x approaches infinity of 3x+1/2

x \to \infty lim (3 x + \frac{1}{2})

integral of 2/(x^2-2x)

\int \frac{2}{x ^{2} - 2 x} d x

derivative of x/(log_{10(x)})

\frac{d}{d x} (\frac{x}{lo g _{10} ( x )})

derivative of y= 1/(log_{4)(x)}derivative of

y = \frac{1}{lo g _{4} ( x )}

Frequently Asked Questions (FAQ)

What is the integral of (2y+3)^2 ?
The integral of (2y+3)^2 is (4y^3)/3+6y^2+9y+C