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Popular Calculus >

integral of (5x-3)^2

Solution

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

Solution

\frac{25 x ^{3}}{3} - 15 x^{2} + 9 x + C

Solution steps

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

Expand

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

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

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

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

\int 9 d x = 9 x

= \frac{25 x ^{3}}{3} - 15 x^{2} + 9 x

Add a constant to the solution

= \frac{25 x ^{3}}{3} - 15 x^{2} + 9 x + C

Graph

Popular Examples

integral of (x^2+sqrt(x^3)+3)/(sqrt(x))

\int \frac{x ^{2} + x ^{3} + 3}{x} d x

integral of (3-4x)

\int (3 - 4 x) d x

integral of (x^2+2x-1)/(x^3-27)

\int \frac{x ^{2} + 2 x - 1}{x ^{3} - 27} d x

integral of sqrt(x^3)+2x^2-x+2/(x^2)

\int x^{3} + 2 x^{2} - x + \frac{2}{x ^{2}} d x

integral of (2x-1)/(sqrt(x))

\int \frac{2 x - 1}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of (5x-3)^2 ?
The integral of (5x-3)^2 is (25x^3)/3-15x^2+9x+C