If `=int(tan^(5)dx=Atan^(4)x-1/2tan^(2)x+B"ln"|secx|+C)` then

Options

A. `A=1/4`
B. `A=1/2`
C. B=1
D. `B=-1`

Explanation

To solve the integral \(\int \tan^5 x \, dx\) and express it in the form \(A \tan^4 x - \frac{1}{2} \tan^2 x + B \ln |\sec x| + C\), we will follow these steps:

### Step 1: Rewrite \(\tan^5 x\)
We can express \(\tan^5 x\) as \(\tan^3 x \cdot \tan^2 x\). Using the identity \(\tan^2 x = \sec^2 x - 1\), we can rewrite the integral:
\[ \int \tan^5 x \, dx = \int \tan^3 x (\sec^2 x - 1) \, dx \]

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