Q. Primitive of $\frac{1}{4\sqrt{x} + x}$ is equal to
A) $2\log{|1 + 4\sqrt{x}|} + c$
B) $\frac{1}{2}\log{|4 - \sqrt{x}|} + c$
C) $2\log{|4 + \sqrt{x}|} + c$
D) $\frac{1}{2}\log{|4 + \sqrt{x}|} + c$
Explanation
(c)
Let $I = \int_{}^{}\frac{1}{\sqrt{x}(4 + \sqrt{x})}dx$
Put $4 + \sqrt{x} = t$
$\Rightarrow \ \frac{1}{2\sqrt{x}}dx = dt$
$\Rightarrow \ \frac{1}{\sqrt{x}}dx = 2dt$
$\therefore\ \ I = 2\int_{}^{}\frac{1}{t}dt = 2\log{|4 + \sqrt{x}|} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.