Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 395: 17

$$\int e^{-5x}sin\,x\,dx=-\frac{e^{-5x}}{26}(cos\,x+5sin\,x)+C$$

$$\int e^{-5x}sin\,x\,dx=-e^{-5x}cos\,x-5e^{-5x}sin\,x-25\int e^{-5x}sin\,x\,dx$$ $$26\int e^{-5x}sin\,x\,dx=-e^{-5x}cos\,x-5e^{-5x}sin\,x$$ $$\int e^{-5x}sin\,x\,dx=-\frac{e^{-5x}}{26}(cos\,x+5sin\,x)+C$$