Solution
= Solution
The derivative of $\ln\cosh x$ is $\tanh x$. Since $\cosh(\ln2)=(2+1/2)/2=5/4$,
$$
\boxed{\int_0^{\ln2}\tanh x\,dx=[\ln\cosh x]_0^{\ln2}=\ln\frac54.}
$$
= Solution
The derivative of $\ln\cosh x$ is $\tanh x$. Since $\cosh(\ln2)=(2+1/2)/2=5/4$,
$$
\boxed{\int_0^{\ln2}\tanh x\,dx=[\ln\cosh x]_0^{\ln2}=\ln\frac54.}
$$