Evaluate :- \(\int \frac{sec^2\sqrt x}{\sqrt{x}}\,dx\)

1.	Evaluate :- \(\int \frac{sec^2\sqrt x}{\sqrt{x}}\,dx\)
Answer» Let \(\sqrt x\) = z ⇒ \(\frac{1}{2\sqrt x}\,dx=dz\) ⇒ \(\frac{dx}{\sqrt x} =2dz\) ∴ \(\int \frac{sec^2\sqrt x}{\sqrt{x}}\,dx\) = \(2\int sec^2z\,dz\) = tan z + C = 2 tan \(\sqrt{x}+C\)

Answer»

Let \(\sqrt x\) = z

⇒ \(\frac{1}{2\sqrt x}\,dx=dz\)

⇒ \(\frac{dx}{\sqrt x} =2dz\)

∴ \(\int \frac{sec^2\sqrt x}{\sqrt{x}}\,dx\) = \(2\int sec^2z\,dz\)

= tan z + C

= 2 tan \(\sqrt{x}+C\)

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