# Integration involving trig. substitution

by Mangoes
Tags: integration, involving, substitution, trig
 Mentor P: 21,413 Your work looks good, and nothing immediately pops out at me. I think that you have a constant wrong somewhere. I'll take a closer look and see if I can spot where the problem is. I suppose trig substitution could be applied to any integral, but where it's most commonly used is where you have the square root of a sum or difference of squares. The radical can appear in the numerator, but commonly appears in the denominator. The idea with trig substitution is to apply the substitution to get an integral that you can actually evaluate, so I don't see it used with cube roots, or the like, or with simple polynomials or power functions, as in your example. LaTeX isn't hard to use. Here's the LaTeX for the integral you started with. To make it actually render, put a pair of $signs at the beginning, and another pair at the end. \int \sqrt{9 + 16x^2}dx Edit: Dick beat me to it, so I won't take a closer look. P: 86 Integration involving trig. substitution  Quote by Dick You are messing up in the integration by parts section. Otherwise, well done! You are partially ignoring the presence of the 9/4 factor. Try it this way. Just integrate sec^3 by parts. Add the 9/4 factor later. Thank you! I followed your suggestion and saw that the result I had was indeed different than what I had previously gotten. After multiplying that by 9/4, differentiating gives my original function.  Quote by Mark44 Your work looks good, and nothing immediately pops out at me. I think that you have a constant wrong somewhere. I'll take a closer look and see if I can spot where the problem is. I suppose trig substitution could be applied to any integral, but where it's most commonly used is where you have the square root of a sum or difference of squares. The radical can appear in the numerator, but commonly appears in the denominator. The idea with trig substitution is to apply the substitution to get an integral that you can actually evaluate, so I don't see it used with cube roots, or the like, or with simple polynomials or power functions, as in your example. LaTeX isn't hard to use. Here's the LaTeX for the integral you started with. To make it actually render, put a pair of$ signs at the beginning, and another pair at the end. \int \sqrt{9 + 16x^2}dx Edit: Dick beat me to it, so I won't take a closer look.