`IfI_n=int_0^pie^x(sin"x")^("n")dx ,t h e n(I_3)/(I_1)"is equal to"` `3/5` (b) `1/5` (c) 1 (d) `2/5`

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

If I_(n)=int(sin x)^(n)dx,n in N, then 5I_(4)-6I_(6) is equal to

If I_(n)=int_(1)^(e)(log x)^(n) d x, then I_(n)+nI_(n-1) equal to

If I_(n)=int x^(n)e^(x)dx, then I_(5)+5I_(4)=

If I_(n)=int_(0)^(1)(1-x^(5))^(n)dx, then (55)/(7)quad (I_(10))/(I_(11)) is equal to

If I_(n)=int sin^(n)x backslash dx, then nI_(n)-(n-1)I_(n-2) equals

L e tI_1=thetaint_0^1(e^xdx)/(1+x)a n dI_2thetaint_0^1(x^2dx)/(e^x^3(2-x^3))dott e h n(I_1)/(I_2)i se q u a lto 3/e (b) e/3 (c) 3e (d) 1/(3e)