Integrating functions is one of the core applications of calculus. Sometimes, this is straightforward, as in:

In a comparatively complicated example of this type, you can use a version of the basic formula for integrating indefinite integrals:

where ​A​ and ​C​ are constants.

Thus for this example,

On the surface, integrating a square root function is awkward. For example, you may be stymied by:

But you can express a square root as an exponent, 1/2:

The integral therefore becomes:

to which you can apply the usual formula from above:

Sometimes, you may have more than one term under the radical sign, as in this example:

You can use ​u​-substitution to proceed. Here, you set ​u​ equal to the quantity in the denominator:

Solve this for ​x​ by squaring both sides and subtracting:

This allows you to get dx in terms of ​u​ by taking the derivative of ​x​:

Substituting back into the original integral gives

Now you can integrate this using the basic formula and expressing ​u​ in terms of ​x​: