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Popular >

integral of (3x+5)^2

Solution

\int (3 x + 5)^{2} d x

Solution

3 x^{3} + 15 x^{2} + 25 x + C

Solution steps

\int (3 x + 5)^{2} d x

Expand

(3 x + 5)^{2} : 9 x^{2} + 30 x + 25

= \int 9 x^{2} + 30 x + 25 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 9 x^{2} d x + \int 30 x d x + \int 25 d x

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

\int 30 x d x = 15 x^{2}

\int 25 d x = 25 x

= 3 x^{3} + 15 x^{2} + 25 x

Add a constant to the solution

= 3 x^{3} + 15 x^{2} + 25 x + C

Graph

Popular Examples

derivative of x^2-3x-5x^{-1}+7x^{-2}

\frac{d}{d x} (x^{2} - 3 x - 5 x^{- 1} + 7 x^{- 2})

(dy)/(dx)=(x^2-3)/(6y^2)

\frac{d y}{d x} = \frac{x ^{2} - 3}{6 y ^{2}}

integral from 0 to 1 of x/(x+1)

\int_{0}^{1} \frac{x}{x + 1} d x

integral of (2t)^{-1/2}

\int (2 t)^{- \frac{1}{2}} d t

integral from-2 to sin(x) of 3t

\int_{- 2}^{s i n (x)} 3 t d t

Frequently Asked Questions (FAQ)

What is the integral of (3x+5)^2 ?
The integral of (3x+5)^2 is 3x^3+15x^2+25x+C