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Chapter 8: Problem 8

Find the indefinite integral. $$ \int \cos 6 x d x $$

Short Answer

Expert verified
\(\sin 6x / 6 + C\).

Step by step solution

01

Identify the inner function

In the integral \(\int \cos 6x dx\), the inner function is \(6x\). The outer function is \(\cos x\). The coefficient '6' of 'x' in the inner function will affect the integration result.
02

Integrate the outer function and divide by the derivative of the inner function

The integral of the outer function (\(\cos x\)) is \(\sin x\), and the derivative of the inner function (6x) is 6. Therefore, the integral of \(\cos 6x\) with respect to \(x\) is \(\sin 6x / 6\).
03

Add the constant of integration

After performing the integration, it's necessary to add a constant of integration, usually denoted as +C. So, the final result of the indefinite integral \(\int \cos 6x dx\) is \(\sin 6x / 6 + C\).

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