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Popular >

integral of (5x-1)^2

Solution

\int (5 x - 1)^{2} d x

Solution

\frac{25 x ^{3}}{3} - 5 x^{2} + x + C

Solution steps

\int (5 x - 1)^{2} d x

Expand

(5 x - 1)^{2} : 25 x^{2} - 10 x + 1

= \int 25 x^{2} - 10 x + 1 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 10 x d x + \int 1 d x

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

\int 10 x d x = 5 x^{2}

\int 1 d x = x

= \frac{25 x ^{3}}{3} - 5 x^{2} + x

Add a constant to the solution

= \frac{25 x ^{3}}{3} - 5 x^{2} + x + C

Graph

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\int \frac{1}{cos ^{2} ( 2 x - 1 )} d x

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\int x ln (x^{4} - 1) d x

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\int t 3 2 t + 7 d t

integral of sin(x)x^3

\int sin (x) x^{3} d x

integral of (sin^5(5x)+cos^3(5x))

\int (sin^{5} (5 x) + cos^{3} (5 x)) d x

Frequently Asked Questions (FAQ)

What is the integral of (5x-1)^2 ?
The integral of (5x-1)^2 is (25x^3)/3-5x^2+x+C