Basic Maths Grand Test- Q17

0 votes

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

A. -cot(e{x^x}) + C

B. tan(x{e^x}) + C

C. tan({e^x}) + C

D. cot({e^x}) + C

asked Nov 18 in Basic Maths by gbmentor (85,520 points)
reshown Nov 20 by getgatebook

1 Answer

0 votes

ANS B.

Let e^x * x= t

Therefore  e^x*1+ e^x*x   dx = dt 

therefore  e^x (1+x) dx= dt

Therefore given integration becomes-

Integration ( dt / cos ^2 t)= interation ( sec^2t dt) = tan(t) +C where t= e^x * x

So =  tan(e^x *x) +C

answered Nov 20 by bhargavakapilpro20 (13,760 points)
Answer:
...