Problem with integration

[MatheusDiasMecatronico]

Hello everyone!
In a mechanical problem I came across with a integration that I could not neither solve it nor understand the solution. Can someone help me, please?

integrate 1 / (x^2 - 0.01)^(1/2) dx

Thank you.

 

[Deleted member 4993]

Hello everyone!
In a mechanical problem I came across with a integration that I could not neither solve it nor understand the solution. Can someone help me, please?

integrate 1 / (x^2 - 0.01)^(1/2) dx

Thank you.

This problem is easily solved with trigonometric substitution. Substitute:

x = 0.1 * sec(t)

dx = 0.1 * sec(t) * tan(t) dt

Be careful to convert the limits of integration also - if one was given.

 

[MarkFL]

A hyperbolic trig. substitution would also work:

[MATH]x=\frac{1}{10}\cosh(t)\implies dx=\frac{1}{10}\sinh(t)\,dt[/MATH]

 

[Steven G]

If you are not studying calculus then you can look up the solution on an integral table.

The integrand will be 1/(x²-a²)^1/2