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Popular Calculus >

integral of (5x+2)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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