JEE Mains · Maths · STD 12 - 7.1 indefinite integral
The integral \(\int {\frac{{3{x^{13}}\, + \,\,2{x^{11}}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^4}}}dx} \) is equal to (where \(C\) is a constant of integration)
- A \(\frac{{{x^4}}}{{6{{(2{x^4}\, + \,3{x^2}\, + \,1)}^3}}}\,\, + \,\,C\)
- B \(\frac{{{x^{12}}}}{{6{{(2{x^4}\, + \,3{x^2}\, + \,1)}^3}}}\,\, + \,\,C\)
- C \(\frac{{{x^4}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^3}}}\,\, + \,\,C\)
- D \(\frac{{{x^{12}}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^3}}}\,\, + \,\,C\)
Answer & Solution
Correct Answer
(B) \(\frac{{{x^{12}}}}{{6{{(2{x^4}\, + \,3{x^2}\, + \,1)}^3}}}\,\, + \,\,C\)
Step-by-step Solution
Detailed explanation
\(\int \frac{3 x^{13}+2 x^{11}}{\left(2 x^{4}+3 x^{2}+1\right)^{4}} d x\) \(\int \frac{\left(\frac{3}{x^{3}}+\frac{2}{x^{5}}\right) d x}{\left(2+\frac{3}{x^{2}}+\frac{1}{x^{4}}\right)^{4}}\) \(\text { Let }\left(2+\frac{3}{x^{2}}+\frac{1}{x^{4}}\right)=t\)…
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