Evaluate the following integrals :\(\int\frac{cos\sqrt x}{\sqrt x}\)dx

1.	Evaluate the following integrals :\(\int\frac{cos\sqrt x}{\sqrt x}\)dx
Answer» Assume, √x = t d(√x) = dt ⇒ \(\frac{1}{2\sqrt x}\) dx = dt ⇒ \(\frac{1}{\sqrt x}\) dx = 2dt Substituting t and dt ⇒2 \(\int\) cost dt = 2sint + c But, √x = t ⇒2 sin(√x) + c.

Answer»

Assume,

√x = t

d(√x) = dt

⇒ \(\frac{1}{2\sqrt x}\) dx = dt

⇒ \(\frac{1}{\sqrt x}\) dx = 2dt

Substituting t and dt

⇒2 \(\int\) cost dt

= 2sint + c

But,

√x = t

⇒2 sin(√x) + c.

Discussion