What is the integral of xsqrt(x^2+25) ?

The integral of xsqrt(x^2+25) is 1/3 (x^2+25)^{3/2}+C

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integral of xsqrt(x^2+25)

\int x x^{2} + 25 d x

\frac{1}{3} (x^{2} + 25)^{\frac{3}{2}} + C

Solution steps

\int x x^{2} + 25 d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = x^{2} + 25

= \frac{( x ^{2} + 25 ) ^{3}}{3}

Simplify

\frac{( x ^{2} + 25 ) ^{3}}{3} : \frac{1}{3} (x^{2} + 25)^{\frac{3}{2}}

= \frac{1}{3} (x^{2} + 25)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (x^{2} + 25)^{\frac{3}{2}} + C

\int 5 x^{4} y^{3} - x^{2} y^{6} + 6 x^{5} - 4 y d x

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

x \to 0 + lim (x ln (x))

\frac{d}{d x} (sin (6 x) cos (4 x))

x^{4} + y^{3} x^{5} + 5 y^{^{'}} = 0

What is the integral of xsqrt(x^2+25) ?
The integral of xsqrt(x^2+25) is 1/3 (x^2+25)^{3/2}+C