Problem 24 - Essential Calculus

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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:\[\int(\sec t+\tan t) dt \]

Step 2: 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.

Step 3: 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.