calculus. How to integrate?

Question

Evaluate the definite integral. The boundary is from 0 to √3/5

 

∫ 1/(1+25x²) dx

Answer 1

Set u= 5x therefore u²=25x².  When you do that you can use substitution and say u =5x du = 5 dx or dx=du/5.  

 

You will get something like the ∫ 1/(1+u²) du/5

 

To integrate this look at your table of integrals to find out this is an arc tan and when you integrate it you will get 1/5 arctan u + c.  Substitute 5x back for you and you have the answer.  Now plug in the numbers to get the final result.