Find the integral involving secant and tangent. (Remember to use absolute values where appropriate.)
 
fraction: 3 (tan(*x*))2    

/ sec(*x*)

 *dx*
 

We are asked to find the integral of the function involving secant and tangent:

\[
\int \frac{3 \tan^2(x)}{\sec(x)} \, dx
\]

### Step 1: Express everything in terms of \(\sin(x)\) and \(\cos(x)\)

Recall the following trigonometric identities:

\[
\tan(x) = \frac{\sin(x)}{\cos(x)} \quad \text{and} \quad \sec(x) = \frac{1}{\cos(x)}
\]

Substitute these into the integrand:

\[
\int \frac{3 \tan^2(x)}{\sec(x)} \, dx = \int 3 \frac{\left(\frac{\sin(x)}{\cos(x)}\right)^2}{\frac{1}{\cos(x)}} \, dx
\]

Simplify the expression:

\[
\int 3 \frac{\sin^

Find the integral involving secant and tangent. fraction: 3 (tan(x))^2 / sec(x) dx

Learn how to find the integral of 3 (tan^2(x)) / sec(x) dx using trigonometric identities such as tan(x) = sin(x) / cos(x) and sec(x) = 1 / cos(x). This step-by-step solution explores integral calculus techniques and is ideal for students in Calculus I.

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