Question

Evaluate each integral. $$\int \cos x \sinh (\sin x) d x$$

   Evaluate each integral.
$$\int \cos x \sinh (\sin x) d x$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 6, Problem 43

Instant Answer

Solved by Expert Tyler Moulton

06/17/2021

Step 1

Step 1: We are given the integral $$\int \cos x \sinh (\sin x) d x$$ We can see that the integral is in the form of $$\int f'(x)g(f(x)) dx$$ where $f'(x) = \cos x$ and $g(f(x)) = \sinh (\sin x)$. Show more…

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Evaluate each integral. $$\int \cos x \sinh (\sin x) d x$$

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Key Concepts

Integration of Composite Functions

This involves recognizing and working with functions composed of an inner and an outer function. When the derivative of the inner function appears in the integrand, it allows the substitution method to simplify the integration process.

u-Substitution

This is a technique in integration where a new variable is introduced to simplify the integral, especially when the derivative of an inner function is present in the integrand. It effectively reverses the chain rule in differentiation.

Hyperbolic Functions

Understanding the properties of hyperbolic functions, such as sinh, is crucial when integrating expressions that include them. These functions often bear similarities to trigonometric functions, which helps in applying standard integration techniques.

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