e^x(1+x)/²(e^x x)dx equals - NCERT Class XII Mathematics Chapter ...

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answer in Exercises 84 and 85.

Question : 85 of 271

Marks: +1, -0

\int \frac{e^x(1+x)}{\cos^2(e^x x)}dx

equals

Solution:

Let

I = \int \frac{e^x(1+x)}{\cos^2(e^x x)}dx

Put

x e^x = t

\Rightarrow (e^x \cdot 1 + e^x x) dx = dt

\therefore I = \int \frac{dt}{\cos^2 t}

= \int \sec^2 t dt

= \tan t + C

= \tan(x e^x) + C

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