AP EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{(x+100) \sqrt{x+99}}=f(x)+c \Rightarrow f(x)\)
- A \(2(x+100)^{1 / 2}\)
- B \(3(x+100)^{1 / 2}\)
- C \(2 \tan ^{-1}(\sqrt{x+99})\)
- D \(2 \tan ^{-1}(\sqrt{x+100})\)
Answer & Solution
Correct Answer
(C) \(2 \tan ^{-1}(\sqrt{x+99})\)
Step-by-step Solution
Detailed explanation
Let \[ \begin{aligned} I & =\int \frac{d x}{(x+100) \sqrt{x+99}} \\ & =\int \frac{d x}{\left.(\sqrt{x+99})^2+1\right) \sqrt{x+99}} \end{aligned} \] Put \(\sqrt{x+99}=t \Rightarrow \frac{1}{\sqrt{x+99}} d x=2 d t\)…
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