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,

## Integration of Basic Square Root Functions

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:

## Integration of More Complex Square Root Functions

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*: