   Chapter 4.5, Problem 18E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ sin x sin ( cos x )   d x

To determine

To evaluate:

The indefinite integral sinx sin(cosx) dx

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

sinx=-cosx +C

2) Given:

sinx sin (cosx) dx

3) Calculation:

Here, use the substitution method because the differential of the function cosx  (-sinx ) is present in the integral except minus sign.

Substitute u=cosx.

Differentiate u=cosx with respect to x

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