What is the integral of sqrt(x^4-10x^2+25) ?

The integral of sqrt(x^4-10x^2+25) is x(x+sqrt(5))(x-sqrt(5))-(2x^3)/3+C

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integral of sqrt(x^4-10x^2+25)

\int x^{4} - 10 x^{2} + 25 d x

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

Solution steps

\int x^{4} - 10 x^{2} + 25 d x

Simplify

x^{4} - 10 x^{2} + 25 : (x + 5) (x - 5)

= \int (x + 5) (x - 5) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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