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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Match the following ∫ f(x) dx is equal to, if Column-I Column-II...

Match the following ∫f(x)dx\int f(x) dx is equal to, if
Column-IColumn-II
(A) \displaystyle f(x) = 1(x2+1)x2+2\frac{1}{(x^2 + 1)\sqrt{x^2 + 2}}(P) \displaystyle x55(1−x4)5/2+\frac{x^5}{5(1 - x^4)^{5/2}} +C
(B) \displaystyle f(x) = 1(x+2)x2+6x+7\frac{1}{(x + 2)\sqrt{x^2 + 6x + 7}}(Q) \displaystyle \sin^{-1} \left( \frac{x + 1}{(x + 2)\sqrt{2}} \right) +C</td></tr><tr><td>(C)f(x)=C</td></tr><tr><td>(C) \displaystyle f(x) =\frac{x^4 + x^8}{(1 - x^4)^{7/2}}</td><td>(R)(</td><td>(R) \displaystyle (\sqrt{x} -2)2)\sqrt{1 - x} + \cos^{-1}\sqrt{x} +C</td></tr><tr><td>(D)f(x)=C</td></tr><tr><td>(D) \displaystyle f(x) =\sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}}</td><td>(S)−tan⁡−1</td><td>(S) \displaystyle -\tan^{-1}\sqrt{1 + \frac{2}{x^2}} +C</td></tr><tr><td></td><td>(T)C</td></tr><tr><td></td><td>(T) \displaystyle\frac{x^6}{6(1 - x^4)^{5/2}} +C</td></tr></table>C</td></tr></table>

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