The integral is equal to :

Question

The integral  is equal to :

Canvas Classes · Accepted Answer

🧠 The  Is a Perfect  in Disguise

Read the integrand. The denominator has  multiplied by . The presence of  inside the arctan is a huge hint. Your first move should be to relate  to .

Compute: . Multiply by : . So
.

Now look at the numerator: . And . So , meaning .

So the whole integrand is .

Two substitutions chained:  (kills the -dependence), then  (kills the ). Final integrand is .

This is the habit I want you to build. When you see  in the denominator with -type expressions elsewhere,

More questions from this chapter