Integrating hyperbolic and inverse functionsEdexcel International A Level Further Maths: Mind map

Exam questions on Integrating hyperbolic and inverse functions

1. A student is working with the integral $I=\int_0^{\ln2}\cosh2x\,dx$.
   Hence find the exact value of $\int_0^{\ln2}\sinh^2x\,dx$.2 marks
2. Integration by parts is used to integrate the product of $x$ with a hyperbolic function.
   Find $\int x\sinh x\,dx$.2 marks
3. Let $I=\int_0^{4/3}\operatorname{arsinh}x\,dx$.
   Use integration by parts to find $\int\operatorname{arsinh}x\,dx$.3 marks