e*(a+(1)/(2))^(2)+(2a-(3)/(a))^(2)

The value of int_(1)^(e)(((x)/(e))^(2x)+((e)/(x))^(x))log_(e)xdx is equal to (A)e-(1)/(2e^(2))-(1)/(2)(B)e-(1)/(2e^(2))+(1)/(2)(C)e^(3)-(1)/(2e^(2))-(1)/(2)(D) none of these ^(2)

The sum of the series (1^(2))/(2!)+(2^(2))/(3!)+(3^(2))/(4!)+ is e+1 b.e-1 c.2e+1 d.2e-1

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

I:2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...]=log_(e)2 II:2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=log_(e)2

Let E=(1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+"......" Then,

int_(-1)^((1)/(2))(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to (sqrt(e))/(2)(sqrt(3)+1) (b) (sqrt(3e))/(2)sqrt(3e)(d)sqrt((e)/(3))

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

int(e^((x)/(2))-1)^(3)e^((x)/(2))dx