wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that I=ex(1+nxn1x2n)(1xn1x2n)dx=ex1+xn1xn.

Open in App
Solution

Let I=ex(1+nxn1x2n)(1xn)1x2ndx
=ex(1x2n(1xn)1x2n+nxn1(1xn)1x2n)
Let f(x)=1x2n(1xn)1x2n

f(x)=(1xn)(1+xn)(1xn)(1xn)(1+xn)

f(x)=1+xn1xn
f(x)=nxn1(1xn)1x2n
I=ex[f(x)+f(x)]dx
I=exf(x)

I=ex1+xn1xn+C

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Integration of Irrational Algebraic Fractions - 1
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon