Expand in ascending powers of x. `(xe^(7x)-e^(-x))/(e^3x)`

Expand in ascending powers of x. 2^x ,

Expand in ascending powers of sin x,

Expand in ascending powers of x. cos x,

int (e^(4x)(dx)/(e^(4x)-5)

int(e^x+e^(-x))/(e^x-e^(-x))dx

Find the least value of f(x) = e^(x) + e^(-x) .

Differentiate (e^x+e^(-x))/(x^2+1)

Integrate int(e^(x-1)+x^(e-1))/(e^x+x^e)dx

Evaluate the following integrals int_0^1(e^x-e^(-x))/(e^x+e^(-x))dx

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .