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Popular >

integral of (4x-5)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

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

\int 25 d x = 25 x

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

Add a constant to the solution

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

Popular Examples

integral of (14x^3+2x+1)/(x^3)

\int \frac{14 x ^{3} + 2 x + 1}{x ^{3}} d x

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\int (- \frac{3}{x}) d x

integral of xsin(1x)

\int x sin (1 x) d x

integral of x^3e^{x^4+3}

\int x^{3} e^{x^{4} + 3} d x

integral of sqrt(6x+1)

\int 6 x + 1 d x

Frequently Asked Questions (FAQ)

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