Tangent Substitution: x over 3/2 power of quadratic: Find .

Here we can use the Tangent Substitution Rule with :

Let , ,

and using the Tangent-Secant identity, .

Upon substitution, we have

.

Now, using the Tangent-Sine-Cosine and the Secant-Cosine identities, we get

.

We can use the Sine Integral to get:

.

Using the Tangent Diagram, we can convert back to an expression in x:

.