Integrals with trig substitutions =p

[reaiy]

NVM I GET HOW TO DO I TNOW

Homework Statement

"The region bounded by the graphs of $$y = \frac{x}{\sqrt{x^2+25}}$$, y = 0, and x = 5 is revolved about the y-axis. Find the volume of the resulting solid."

Homework Equations

The only way i see to do this right now is to use shells, and the equation for that is

$$V = \int 2 \pi x f(x)$$ where the integral is from the lower limit to the upper limit
Mathematica can't find an answer to it. You can try it yourself if you want [Integral of 2*pi*x^2/(x^2+25)^(1/2)]Thanks in advance for your helpOh also, the correct answer is $$25\pi[\sqrt{2}-\ln{\sqrt{2}+1}] \approx 41.85$$
EDIt: ok mathematica does get an answer, but is the a way to find it without a reduction formula for tanx^2*secx ?

 

[LCKurtz]

I get an integrand containing

$$\frac{\tan^2\theta}{\sec\theta}= \frac{\sec^2\theta - 1}{\sec\theta}=\sec\theta-\cos\theta$$

Do you know how to integrate $\sec\theta$?