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Popular >

integral of (9x+4)^2

Solution

\int (9 x + 4)^{2} d x

Solution

27 x^{3} + 36 x^{2} + 16 x + C

Solution steps

\int (9 x + 4)^{2} d x

Expand

(9 x + 4)^{2} : 81 x^{2} + 72 x + 16

= \int 81 x^{2} + 72 x + 16 d x

Apply the Sum Rule:

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

= \int 81 x^{2} d x + \int 72 x d x + \int 16 d x

\int 81 x^{2} d x = 27 x^{3}

\int 72 x d x = 36 x^{2}

\int 16 d x = 16 x

= 27 x^{3} + 36 x^{2} + 16 x

Add a constant to the solution

= 27 x^{3} + 36 x^{2} + 16 x + C

Popular Examples

integral from 1 to infinity of xe^x

\int_{1}^{\infty} x e^{x} d x

y^{''}-4y^'+4y=e^x

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x}

limit as x approaches 2 of 825

x \to 2 lim (825)

derivative of y=e^{-x/2}derivative of

y = e^{- \frac{x}{2}}

d/(dy)(arctan(y/x))

\frac{d}{d y} (arctan (\frac{y}{x}))

Frequently Asked Questions (FAQ)

What is the integral of (9x+4)^2 ?
The integral of (9x+4)^2 is 27x^3+36x^2+16x+C