sum_(i)^(n+1)int(x^(3)+x+1)/(x^(2)-1)dx

I=int(1-x^(2))/(x(1-2x))dx

int(2x^(n-1))/(x^(n)+3)dx

I=int(1)/(x^(3)+x^(2)+x+1)dx

(i)int(x^(3)-1)/(x^(2))dx(ii)int(x^(2/3)+1)dx

If I=sum_(k=2)^(10)int_(k)^(k^(2))(k-1)/(x(x-1))dx, then

Evaluate : (i) inte^(x)((1)/(x)-(1)/(x^(2)))dx (ii) inte^(x)((1)/(x^(2))-(2)/(x^(3)))dx (iii) inte^(x){sin^(-1)x+(1)/(sqrt(1-x^(2)))}dx (iv) inte^(x)(tanx+logsecx)dx

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

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

(i) int ((1+x)^(3))/(sqrt(x))dx " "(ii) int((1+x)^(3))/(x^(4)) dx