`inte^(msin^-1x)dx`

Evaluate: (i) int5^x+tan^((-1)x)((x^2+2)/(x^2+1))\ dx (ii) int(e^msin^((-1)x))/(sqrt(1-x^2))\ dx

int (tan^(-1)x)dx

Differentiate the following w.r.t.x. sin(msin^(-1)x),|x|lt1

(i) int(tan^(-1))/((1+x^(2)))dx" "(ii) int(1)/(sqrt(1-x^(2)) sin^(-1)x)dx

If y=e^(msin^(-1)x) prove that (1-x^2)((d^2y)/dx^2)-x(dy)/dx=m^2y

Evaluate the following : (i) int(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx " (ii) " int(sqrt(2+logx))/(x)dx (iii) int((sin^(-1)x)^(3))/(sqrt(1-x^(2)))dx " (iv) " int(cotx)/(sqrt(sinx))dx

int sec^(-1)x dx

int(1)/(e^(-x)) dx

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

Evaluate the following: (i) int(sec^(2)x)/(3+tanx)dx " (ii) " int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx (iii) int(1-tanx)/(1+tanx)dx " (iv) " int(1)/(1+e^(-x))dx