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Chapter 4: Problem 24

Find the indefinite integral. $$ \int(\sec t+\tan t) d t $$

Short Answer

Expert verified
\[ \ln |\sec t + \tan t| + C \]

Step by step solution

01

Write down the integral

We are asked to find the indefinite integral of \( \sec t + \tan t \). Write it down as it is which looks like:\[\int(\sec t+\tan t) dt \]
02

Recognize the pattern

Recognize the pattern here. The indefinite integral of \( \sec t + \tan t \) is a standard result in integration which is equal to \( \ln |\sec t + \tan t| \). This is a known result in calculus.
03

Write down the solution

Our task then becomes to simply state this standard result:\[\int(\sec t + \tan t) dt = \ln |\sec t + \tan t| + C\]where \( C \) is the constant of integration.

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Most popular questions from this chapter

In Exercises \(88-92,\) verify the differentiation formula. \(\frac{d}{d x}[\cosh x]=\sinh x\)

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Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f\) is continuous on \([a, b]\), then \(f\) is integrable on \([a, b]\).

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