What is the integral of (x^2-10x+25)^{5/2} ?

The integral of (x^2-10x+25)^{5/2} is ((x-5)^6)/6+C

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integral of (x^2-10x+25)^{5/2}

\int (x^{2} - 10 x + 25)^{\frac{5}{2}} d x

\frac{( x - 5 ) ^{6}}{6} + C

Solution steps

\int (x^{2} - 10 x + 25)^{\frac{5}{2}} d x

Simplify

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

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = x - 5

= \frac{( x - 5 ) ^{6}}{6}

Add a constant to the solution

= \frac{( x - 5 ) ^{6}}{6} + C

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What is the integral of (x^2-10x+25)^{5/2} ?
The integral of (x^2-10x+25)^{5/2} is ((x-5)^6)/6+C