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  • Choose the correct answer (e^x(1+x)dx /cos^2(e^xx))

 Q24   Choose the correct answer \int \frac{e ^x ( 1+x)}{\cos ^ 2 ( e ^xx )} dx \: \: equals  

          \\(A) -\cot (ex^x) + C \\\\ (B) \tan (xe^x) + C\\\\ (C) \tan (e^x) + C \\\\ (D) \cot (e^x) + C

Answers (1)

best_answer

The correct option is (B)

Let e^xx = t.
So, (e^x.x+ 1.e^x)dx = dt
(1+x)e^x\ dx =dt
 

therefore,

\int \frac{e^x(1+x)}{\cos^2(e^x.x)}dx =\int\frac{dt}{\cos^2t}
                                    \\=\int \sec^2t dt\\ =\tan t +C\\ =\tan(e^x.x)+C

Posted by

manish

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