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Popular >

integral of (5x+4)^2

Solution

\int (5 x + 4)^{2} d x

Solution

\frac{25 x ^{3}}{3} + 20 x^{2} + 16 x + C

Solution steps

\int (5 x + 4)^{2} d x

Expand

(5 x + 4)^{2} : 25 x^{2} + 40 x + 16

= \int 25 x^{2} + 40 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 25 x^{2} d x + \int 40 x d x + \int 16 d x

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

\int 40 x d x = 20 x^{2}

\int 16 d x = 16 x

= \frac{25 x ^{3}}{3} + 20 x^{2} + 16 x

Add a constant to the solution

= \frac{25 x ^{3}}{3} + 20 x^{2} + 16 x + C

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Frequently Asked Questions (FAQ)

What is the integral of (5x+4)^2 ?
The integral of (5x+4)^2 is (25x^3)/3+20x^2+16x+C