Evaluate : i. ∫[1 + 1/(1 + x^2) - 2/√1 - x^2 + 5/x√x^2 - 1 + a^x]dx

Question

Evaluate :

\(\int[1+\frac{1}{(1+x^2)}-\frac{2}{\sqrt{1-x^2}}+\frac{5}{x\sqrt{x^2-1}}+a^x]dx\) 

∫[1 + 1/(1 + x²) - 2/√1 - x² + 5/x√x² - 1 + a^x]dx

Answer 1

Given:

Since, \(\int \frac{1}{1+x^2}dx=tan^{-1}x+c;\)

So,