1FIND A
5 Answers
29On doing rationalisation u will get..
\int \frac{\sqrt{x-1}+ \sqrt{x+1}}{\sqrt{x-1}-\sqrt{x+ 1}} dx = \int \frac{x-1 +x+1 + 2\sqrt{x^{2}-1}}{x-1 - (x+1)}dx = \int \frac{2x+2\sqrt{x^{2}-1}}{-2}dx
which can be easily evaluated...
1Tried the second one like this :
put ax + b = t2 → adx = 2tdt →dx = 2a t dt
also xn = \left(\frac{t^{2}-b}{a} \right)^{n} then integral reduces to :
\frac{2a^{n}}{a}\int \frac{t}{(t^{2}-b)^{n}t}dt
then {2a^{n-1}}\int{\frac{1}{(t^{2}-b)^{n}}}dt
after that not sure wat to do ................
1i tried by parts but went too long
i considered 1√ax+b as first function and 1xn as second.
May be that's not correct step to proceed but govind agreed with me in taking fuctions for by parts