Evaluate the following integrals :\(\int \frac{sec^2\sqrt x}{\sqrt x}\

1.	Evaluate the following integrals :\(\int \frac{sec^2\sqrt x}{\sqrt x}\)dx
Answer» Assume, √x = t d(√x) = dt ⇒ \(\frac{1}{2\sqrt x}\)dx = dt ⇒ \(\frac{1}{\sqrt x}\) = dt Substituting t and dt ⇒2 ∫ sec²t dt = 2 tan t + c But, √x = t ⇒2 tan(√x) + c.

Evaluate the following integrals :\(\int \frac{sec^2\sqrt x}{\sqrt x}\)dx

Answer»

Assume,

√x = t

d(√x) = dt

⇒ \(\frac{1}{2\sqrt x}\)dx = dt

⇒ \(\frac{1}{\sqrt x}\) = dt

Substituting t and dt

⇒2 ∫ sec²t dt

= 2 tan t + c

But,

√x = t

⇒2 tan(√x) + c.