   Chapter 7.4, Problem 52E

Chapter
Section
Textbook Problem

# Make a substitution to express the integrand as a rational function and then evaluate the integral. ∫ cosh t sinh 2 t + sinh 4 t d t

To determine

To Find: Make a substitution to express the integrand as a rational function and then evaluate the integral coshtsinh2t+sinh4tdt

Explanation

Calculation:coshtsinh2t+sinh4tdt

Let u=sinhtthendu=cosht.dt

Use u substitution

coshtsinh2t+sinh4tdt=1u4+u2du=1(u2)(u2+1)du

Resolving into partial fractions

1(u2)(u2+1)=Au+Bu2+Cu+Du2+1

On solving, we get

A(u3+u)+B(u2+1)+C(

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