JEE Main & Advanced Mathematics Indefinite Integrals Question Bank

done Numerical Value Type Questions - Indefinite Integration Total Questions - 15

• question_answer1)
  If \[\int{\frac{1}{x\sqrt{1-{{x}^{3}}}}dx=a\,\,\log \,\,\left| \frac{\sqrt{1-{{x}^{3}}}-1}{\sqrt{1-{{x}^{3}}}+1} \right|}+b,\] then find value of a.
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• question_answer2)
  If \[\int{\frac{\cos 4x+1}{\cot x-\tan x}dx=-\frac{1}{\lambda }}\cos 4x+B,\]then find value of\[\lambda \].
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• question_answer3)
  If \[\int{\frac{2{{x}^{2}}+3}{\left( {{x}^{2}}-1 \right)\left( {{x}^{2}}-4 \right)}dx=\log {{\left( \frac{x-2}{x+2} \right)}^{a}}{{\left( \frac{x+1}{x-1} \right)}^{b}}+c,}\]then find value of\[a+b\].
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• question_answer4)
  If \[\int{{{e}^{3\log x}}{{\left( {{x}^{4}}+1 \right)}^{-1}}dx=\frac{1}{k}\log \left( {{x}^{4}}+1 \right)+c}\] then find value k.
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• question_answer5)
  If \[\int{{{e}^{x/2}}\sin \left( \frac{x}{2}+\frac{\pi }{4} \right)dx=k{{e}^{x/2}}\sin \frac{x}{2}+c}\] then find k.
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• question_answer6)
  If \[\int{\frac{dx}{2{{x}^{2}}+x+1}=\frac{1}{2}{{\tan }^{-1}}\left( \frac{4x+1}{\sqrt{k}} \right)+c}\] then find k.
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• question_answer7)
  If \[\int{\left( {{\sin }^{4}}x-{{\cos }^{4}}x \right)dx=-\frac{\sin 2x}{k}+c}\] then find k.
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• question_answer8)
  If \[\int{\frac{dx}{\left( 2x-7 \right)\sqrt{{{x}^{2}}-7x+12}}}={{\sec }^{-1}}\left( ax-b \right)+c\] then find \[a+b\].
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• question_answer9)
  If \[\int{f\left( x \right)dx=g\left( x \right)}\] and \[\int{{{x}^{11}}f\left( {{x}^{6}} \right)dx=\frac{1}{a}{{x}^{6}}g\left( {{x}^{6}} \right)-\int{{{x}^{b}}g\left( {{x}^{6}} \right)dx+c}}\] then find \[a+b\].
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• question_answer10)
  If \[\int{\sqrt{\frac{\cos x-{{\cos }^{3}}x}{1-{{\cos }^{3}}x}}dx=k{{\cos }^{-1}}\left( {{\cos }^{3/2}}x \right)+c}\] then find k.
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• question_answer11)
  If \[\int{\frac{{{e}^{5{{\log }_{e}}x}}-{{e}^{4{{\log }_{e}}x}}}{{{e}^{3{{\log }_{e}}x}}-{{e}^{2{{\log }_{e}}x}}}dx=\frac{{{x}^{3}}}{\lambda }+c,}\] then find \[\lambda \].
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• question_answer12)
  If \[\int{\frac{\cos 2x-\cos 2\alpha }{\cos x-\cos \alpha }dx=\lambda \left( \sin x+x\cos \alpha  \right)+c}\] then find\[\lambda \].
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• question_answer13)
  If \[\int{\frac{3x+2}{4{{x}^{2}}+4x+5}dx=p\,\,\ell n(4{{x}^{2}}+4x+5)+q{{\tan }^{-1}}(x+a)+c,}\] then find \[p+q-a\].
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• question_answer14)
  If \[\int{\frac{{{\sin }^{2}}}{{{\cos }^{6}}x}dx}\] is a polynomial in tan x then find degree of polynomial.
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• question_answer15)
  If \[\int{\frac{1+{{x}^{2}}}{\sqrt{1-{{x}^{2}}}}dx=k{{\sin }^{-1}}x-\lambda x\sqrt{1-{{x}^{2}}}+c}\] then find \[k+\lambda \].
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