calculus

The integral of [e^(11x)]/[e^(11x)+8] is ln|e^(11x)+8| + C, where C is an arbitrary constant. This integral can be found using integration by parts. The integral is an application of u-substitution, where the function is changed into the form u = e^(11x). This eliminates the denominator from the integral, leaving the integral in the form of du/11, which when solved results in ln|e^(11x)+8| + C.