If , find the equation of the curve through (1,4).

We have the derivative of the curve, so we can integrate to find y:

Let's try the General Power rule for integrals:
Let , .

Now the integral becomes

We now use the Scalar Multiple rule for integrals to get

Now we can use the General Power rule for integrals to get

Finally we substitute for u (as we defined it above) to get an answer in terms of x:

.

In order to determine a value for C, we can use the fact that the coordinates of the given point must satisfy this equation:
, or .

Now the equation of the curve becomes .