`int(dx)/(e^xsqrt(2e^x-1))=` `2sec^(-1)sqrt(2e^x)+c` `-2tan^(-1)1/(sqrt(2e-1))+c` `2sec^(-1)(sqrt(2)e^x)+c` (d) (2sqrt(2e^x-1))/2e^x`2tan^(-1)sqrt(2e^x-1)+c`

int(dx)/(sqrt(2e^(x)-1))=

intsqrt(e^x-1)dxi se q u a lto 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)+c sqrt(e^x-1)+tan^(-1)sqrt(e^x-1)+c 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c

IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s a. 1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C b. 1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C c. 1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C d. 1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C

Find int(e^(x))/(sqrt(4-e^(2x)))dx

Find the sum cos e c^(-1)sqrt(10)+cos e c^(-1)sqrt(50)+cos e c^(-1)sqrt(170)++cos e c^(-1)sqrt((n^2+1)(n^2+2n+2))

Evaluate: int1/(sqrt(e^(5x))(4sqrt(e^(2x)+e^(-2x))^3 )

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto (sqrt(e))/2(sqrt(3)+1) (b) (sqrt(3e))/2 sqrt(3e) (d) sqrt(e/3)

Prove that (tan^(-1)1/e)^2+(2e)/((e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^2+1))