JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(f(x)=\int \frac{5 x^{8}+7 x^{6}}{\left(x^{2}+1+2 x^{7}\right)^{2}} d x,(x \geq 0), f(0)=0\) and \(f(1)=\frac{1}{K},\) then the value of \(K\) is
- A \(1\)
- B \(2\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(f(x)=\int \frac{\left(5 x^{8}+7 x^{6}\right) d x}{x^{14}\left(x^{-5}+x^{-7}+2\right)^{2}}\) Let \(x^{-5}+x^{-7}+2=t\) \(\left(-5 x^{-6}-7 x^{-8}\right) d x=d t\) \(\Rightarrow f(x)=\int-\frac{d t}{t^{2}}=\frac{1}{t}+c\) \(f(x)=\frac{x^{7}}{x^{2}+1+2 x^{7}}\)…
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