JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int {\frac{{dx}}{{{{(x + 1)}^{\frac{3}{4}}}{{(x - 2)}^{\frac{5}{4}}}}}} \) is equal to
- A \( - \frac{4}{3}{\left( {\frac{{x + 1}}{{x - 2}}} \right)^{\frac{1}{4}}}\, + \,c\)
- B \(4{\left( {\frac{{x + 1}}{{x - 2}}} \right)^{\frac{1}{4}}}\, + \,c\)
- C \(4{\left( {\frac{{x - 2}}{{x + 1}}} \right)^{\frac{1}{4}}}\, + \,c\)
- D \( - \frac{4}{3}{\left( {\frac{{x - 2}}{{x + 1}}} \right)^{\frac{1}{4}}}\, + \,c\)
Answer & Solution
Correct Answer
(B) \(4{\left( {\frac{{x + 1}}{{x - 2}}} \right)^{\frac{1}{4}}}\, + \,c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{d x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}\) \(\int {\frac{{dx}}{{{{\left( {\begin{array}{*{20}{c}} {x + 1}\\ {x - 2} \end{array}} \right)}^{3/4}}{{(x - 2)}^2}}}} \) \(\text { put } \frac{x+1}{x-2}=t\) \(\frac{{ - 3}}{{{{(x - 2)}^2}}} = \frac{{dt}}{{dx}}\)…
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