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Popular >

integral of (2+5x)^2

Solution

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

Solution

4 x + 10 x^{2} + \frac{25 x ^{3}}{3} + C

Solution steps

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

Expand

(2 + 5 x)^{2} : 4 + 20 x + 25 x^{2}

= \int 4 + 20 x + 25 x^{2} 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 4 d x + \int 20 x d x + \int 25 x^{2} d x

\int 4 d x = 4 x

\int 20 x d x = 10 x^{2}

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

= 4 x + 10 x^{2} + \frac{25 x ^{3}}{3}

Add a constant to the solution

= 4 x + 10 x^{2} + \frac{25 x ^{3}}{3} + C

Popular Examples

integral of (sqrt(x)+2)

\int (x + 2) d x

derivative of 3xe^{-ax}derivative of

3 x e^{- a x}

5t^2y^{''}+ty^'-12y=0

5 t^{2} y^{^{''}} + t y^{^{'}} - 12 y = 0

integral of (x^2)/(sqrt(x^6-9))

\int \frac{x ^{2}}{x ^{6} - 9} d x

slope of (3,0),(6,2)slope

(3, 0), (6, 2)

Frequently Asked Questions (FAQ)

What is the integral of (2+5x)^2 ?
The integral of (2+5x)^2 is 4x+10x^2+(25x^3)/3+C