# int 1/(x^2+5)^(3/2) dx Find the indefinite integral

Recall that indefinite integral follows the formula: int f(x) dx = F(x) +C

where: f(x) as the integrand

F(x) as the anti-derivative function

C  as the arbitrary constant known as constant of integration

For the given problem int 1/(x^2+5)^(3/2)dx , it...

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Recall that indefinite integral follows the formula: int f(x) dx = F(x) +C

where: f(x) as the integrand

F(x) as the anti-derivative function

C  as the arbitrary constant known as constant of integration

For the given problem int 1/(x^2+5)^(3/2)dx , it resembles one of the formula from integration table.  We may apply the integral formula for rational function with roots as:

int 1/(u^2+a^2)^(3/2)du= u/(a^2sqrt(u^2+a^2))+C

By comparing "u^2+a^2 " with "x^2+5 " , we determine the corresponding values as:

u^2=x^2 then u = x and du = dx

a^2 =5 then a = sqrt(5) .

Plug-in the corresponding values on the aforementioned integral formula for rational function with roots, we get:

int 1/(x^2+5)^(3/2)dx =x/(5sqrt(x^2+5))+C

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