AP EAMCET · Maths · Indefinite Integration
\(\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x=\)
- A \(\frac{x^{2021}}{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
- B \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
- C \(\frac{\pi x^{2021}}{2021}+\frac{\pi}{2}+C\)
- D \(\frac{x^{52}}{52}+\frac{\pi}{2}+C\)
Answer & Solution
Correct Answer
(B) \(\frac{x^{2021}}{2021}\left(\tan ^{-1} x+\cot ^{-1} x\right)+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} I & =\int x^{2020}\left(\tan ^{-1} x+\cot ^{-1} x\right) d x \\ & =\int x^{2020}\left(\frac{\pi}{2}\right) d x \quad\left\{\because \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right\} \\ & =\frac{\pi}{2} \frac{x^{2021}}{2021}+C=\frac{x^{2021}}{2021}\left(\tan ^{-1}…
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