Video: Integrating Reciprocal Trigonometric Functions

Determine ∫ (βˆ’ secΒ² 6π‘₯) dπ‘₯.

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Video Transcript

Determine the indefinite integral of negative sec squared six π‘₯ evaluated with respect to π‘₯.

To answer this question, it’s almost simply enough to quote the general result for the integral of sec squared of π‘Žπ‘₯. It’s one over π‘Ž times the tan of π‘Žπ‘₯. It is sensible, though, to take a factor of negative one outside of the integral as shown. And when we do, we obtain the solution to be negative one times a sixth of tan six π‘₯ plus 𝑐. And all that’s left is to distribute the parentheses. Negative one times a sixth of tan six π‘₯ is negative one-sixth tan of six π‘₯. And negative one times 𝑐 gives us this new constant, capital 𝐢. And so we find our indefinite integral to be negative one sixth of tan of six π‘₯ plus 𝐢.

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