If `e^(i theta)= cos theta+isin theta`, find the value of `|(1,e^(ipi//3),e^(ipi//4)),(e^(-ipi//3),1,e^(i2pi//3)),(e^(-ipi//4),e^(-2ipi//3),1)|`

The value of int_(e)^(e^(3))(1)/(x)dx is equal to

int_(-pi/4)^(pi/4)(e^(x)*sec^(2)xdx)/(e^(2x)-1) is equal to

If alpha, beta , gamma are the cube roots of unity, then the value of the determinant |{:(e^a,e^(2a),(e^(3a)-1)), (e^beta,e^(2 beta), (e^(2 beta)-1)), (e^gamma,e^(2gamma), (e^(3 gamma)-1)):}| is equal to

Find the integrals int(4 e^(3x)+1) d x

The real part of e^((3+4i)x) is

Find the following integrals intfrac(2e^x)(e^(3x)-6e^(2x)+11e^x-6

if cos theta_(1) + cos theta_(2) + cos theta_(3)= sin theta_(1) + sin theta_(2) + sin theta_(3)= 0 , then the value of cos (theta_(1) + theta_(2)) + cos (theta_(2) + theta_(3)) + cos (theta_(3) + theta_(1)) is

If z= re^(i theta ) , " then " |e^(iz) | is equal to a)1 b) e^(2r) sin theta c) e^( r sin theta) d) e^(-r sin theta)

The value of the integral int_(0)^(log5)(e^(x)sqrt(e^(x)-1))/(e^(x)+3)dx is