JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int{ \cfrac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}}\) is equal to (where \(\mathrm{C}\) is a constant of integration)
- A \(\left(\frac{x-3}{x+4}\right)^{\frac{1}{7}}+C\)
- B \(-\left(\frac{x-3}{x+4}\right)^{-\frac{1}{7}}+C\)
- C \(\frac{1}{2}\left(\frac{x-3}{x+4}\right)^{\frac{3}{7}}+C\)
- D \(-\frac{1}{13}\left(\frac{x-3}{x+4}\right)^{-\frac{13}{7}}+C\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{x-3}{x+4}\right)^{\frac{1}{7}}+C\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \frac{\mathrm{dx}}{(\mathrm{x}+4)^{\frac{8}{7}}(\mathrm{x}-3)^{\frac{6}{7}}}\)\(=\int \frac{\mathrm{dx}}{\left(\frac{\mathrm{x}+4}{\mathrm{x}-3}\right)^{\frac{8}{7}}(\mathrm{x}-3)^{2}}\) Let \(\frac{\mathrm{x}+4}{\mathrm{x}-3}=\mathrm{t}\)…
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