AP EAMCET · Maths · Indefinite Integration
If \(I_n=\int \tan ^n x d x(n>1)\), then \(I_4+I_6=\)
- A \(\frac{1}{5} \tan ^5 x+C\)
- B \(-\frac{1}{5} \tan ^5 x+C\)
- C \(\frac{1}{10} \tan ^5 x+C\)
- D \(-\frac{1}{10} \tan ^5 x+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{5} \tan ^5 x+C\)
Step-by-step Solution
Detailed explanation
\(\int \tan ^n x d x\) \(\begin{aligned} & I_4+I_6=\int \tan ^4 x d x+\int \tan ^6 x d x \\ & =\int\left(\tan ^4 x+\tan ^6 x\right) d x=\int \tan ^4 x \sec ^2 x d x\end{aligned}\) Let \(\tan x=t \Rightarrow \sec ^2 x d x=d t\)…
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