Ok.
Here is worked out example.
##\int_0^L e^{i2 \pi nx/L}e^{-i2 \pi mx/L} \, dx \rightarrow \int_0^L e^{\frac {i2 \pi nx + -i2 \pi mx} L} \, dx \rightarrow\int_0^L e^{\frac {i2 \pi(n-m)x} L } \, dx##
##a= \frac {i2 \pi(n-m)} L##
##\int e^{ax} \, dx = \frac 1 a e^{ax} \rightarrow##
##\int...