l(alpha)=int_(0)^(1)(x^(alpha)-1)/(ln x)

int_(0)^(1)(x^(alpha)-1)/(log x)dx=

integrate int_(0)^(1)(x^(alpha)-1)/(log x)

Evaluate: int_0^1(x^alpha-1)/log_exdx

Evaluate: int_0^1(x^alpha-1)/log_exdx

If alpha=int_(0)^(1)(e^(9x+3tan^(-1)x)((12+9x^(2))/(1+x^(2)))dx where tan^(-1)x takes only principal values, then the value of (log_(e)|1+alpha|-(3pi)/(4)) is-

If alpha=int_(0)^(1)(e^(9x+3tan^(-1)x))((12+9x^(2))/(1+x^(2)))dx wheretan ^(-1) takes only principal values,then the value of (log_(e)|1+alpha|-(3 pi)/(4))is

int_(0)^(1)(log(1+x))/(1+x)

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , hten