JEE Mains · Maths · STD 12 - 7.1 indefinite integral
\(\text { If } \int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} d x=A\left(\frac{\alpha x-1}{\beta x+3}\right)^B+C,\) where \(\mathrm{C}\) is the constant of integration, then the value of \(\alpha+\beta+20 \mathrm{AB}\) is ...........
- A \(6\)
- B \(7\)
- C \(8\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
\( \int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} d x=A\left(\frac{\alpha x-1}{\beta x+3}\right)^B+C \) \( I=\int \frac{1}{(x-1)^{4 / 5}(x+3)^{6 / 5}} d x \) \( I=\int \frac{1}{\left(\frac{x-1}{x+3}\right)^{4 / 5}(x+3)^2} d x \)…
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