If `I_K=int_1^e(lnx)^kdx(k in I^+)dx(k in I^+),` then find the value of `I_4dot`

Let I_1=int_0^1e^(x^2)dx and I_2=int_0^(12)2^(x^2)e^(x^2)dx then the value of I_1 +I_2 is equal to

I=int_( of k?)^(2 pi)sin^(4)xdx=k int_(0)^( pi/2)cos^(4)xdx find value

Consider I_(1)=int_(10)^(20)(lnx)/(lnx+ln(30-x))dx and I_(2)=int_(20)^(30)(lnx)/(lnx +ln(50-x))dx . Then, the value of (I_(1))/(I_(2)) is

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

Consider I(alpha)=int_(alpha)^(alpha^(2))(dx)/(x) (where alpha gt 0 ), then the value of Sigma_(r=2)^(5)I(r )+Sigma_(k=2)^(5)I((1)/(k)) is

Write the value of hat i( hat jxx hat k)dot

If I_(n)-int(lnx)^(n)dx, then I_(10)+10I_(9) is equal to (where C is the constant of integration)

If the value of the integral I=int_((pi)/(4))^((pi)/(3))" max "(sinx, tanx)dx is equal to ln k, then the value of k^(2) is equa to

If a=2hat(i)+3hat(j)-hat(k), b=-hat(i)+2hat(j)-4hat(k), c=hat(i)+hat(j)+hat(k) , then find the value of (atimesb)*(atimesc) .