Evaluate: `int x e^x cosx dx`

int e^(x)cosx dx

Evaluate: inte^(-x)cosx\ dx

Evaluate: int e^x (cosx-sinx)dx

Evaluate int\ x^5+cosx\dx

Evaluate: inte^x\ (cosx-sinx)\ dx

Evaluate: inte^x(sinx+cosx)dx

Given that int e^x[f(x)+f^'(x)] dx = e^x f(x)+c . Using the given result evaluate int e^x(sinx+cosx)dx

Given that int e^x[f(x)+f^'(x)] dx = e^x f(x)+c . By writing int e^x(sinx+cosx)dx = int e^x sinxdx+ int e^x cosx dx and applying integration by parts in the first integral, evaluate int e^x(sinx+cosx)dx

Evaluate inte^x(cosx-sinx)dx .

Evaluate int (2x^2+cosx+e^x) dx