Search any question & find its solution
Question:
Answered & Verified by Expert
$\int \frac{d x}{\sqrt{x}(x+9)}$ is equal to
Options:
Solution:
2678 Upvotes
Verified Answer
The correct answer is:
$\frac{2}{3} \tan ^{-1}\left(\frac{\sqrt{x}}{3}\right)+C$
Let
$I=\int \frac{d x}{\sqrt{x}(x+9)}$
Put
$\begin{aligned} x & =t^2 \Rightarrow d x=2 t d t \\ & =\int \frac{2 t d t}{t\left(t^2+9\right)}=2 \cdot \frac{1}{3} \tan ^{-1} \frac{t}{3}+C \\ & =\frac{2}{3} \tan ^{-1} \frac{\sqrt{x}}{3}+C\end{aligned}$
$I=\int \frac{d x}{\sqrt{x}(x+9)}$
Put
$\begin{aligned} x & =t^2 \Rightarrow d x=2 t d t \\ & =\int \frac{2 t d t}{t\left(t^2+9\right)}=2 \cdot \frac{1}{3} \tan ^{-1} \frac{t}{3}+C \\ & =\frac{2}{3} \tan ^{-1} \frac{\sqrt{x}}{3}+C\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.