Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 2

$$\cosh (x+1)+C$$

Given $$\int \sinh (x+1) d x$$ Let $$ u=x+1 \ \ \ \to du =dx$$ Then \begin{aligned} \int \sinh (x+1) d x &=\int \sinh u d u \\ &=\cosh u+C \\ &=\cosh (x+1)+C \end{aligned}