Question

Find the general indefinite integral.

\(\int {(\sin x + \sinh x)dx} \)

Short answer

The value of \(\int {(\sin x + \sinh x)dx} \) is \( - \cos x + \cosh + C\).

Step-by-step solution

Indefinite integral.

Consider the following indefinite integral:

\(\int {{\rm{(sinx + sinhx)dx}}} \)

The significance of integral.

The sum of two integral is expressed as,

\(\int {(f(x) + g(x))dx} = \int {f(x)dx} + \int {g(x)dx} \)

Evaluate the given indefinite integral.

\(\)\(\begin{aligned}{c}\int {(\sin x + \sinh x)dx} &= \int {\sin xdx} + \int {\sinh xdx} \\ &= - \cos x + \cosh x + C\end{aligned}\)

Therefore, the value of \(\int {(\sin x + \sinh x)dx} \) is \( - \cos x + \cosh + C\).