<p>What is the antiderivative of (sin u) / (u)?</p>
<p>I don't think there's any simple way of taking that integral. What topic are you studying right now?</p>
<p>(btw, to check my work, I put it into Derive 6, and it doesn't even want to mess with it)</p>
<p>This is not a trivial integral. It is called the sine integral. See MathWorld's entry on it: <a href="http://mathworld.wolfram.com/SineIntegral.html%5B/url%5D">http://mathworld.wolfram.com/SineIntegral.html</a></p>
<p>I seriously doubt this helps, but the definite integral of sin(u)/u from 0 to x can be computed with the series in the following image: <a href="http://upload.wikimedia.org/math/b/0/d/b0d49348406b749045a2873a956a0704.png%5B/url%5D">http://upload.wikimedia.org/math/b/0/d/b0d49348406b749045a2873a956a0704.png</a></p>
<p>Yeah, this integral would not be on an AP Calculus test or anything like that. Worst case scenario, you could always approximate it using Simpson's rule or something.</p>
<p>Hi this is kinda irrelevant, but is Calculus hard? I'm a junior (gr.11) in Canada, and next semester I'm supposed to be taking social studies, physics 11, chemistry 11, and psychology, but there is a new AP calculus class in my school (my school usually doesn't have AP classes unfortunately) so I am thinking of taking the AP Calc course instead of psychology. I am usually very good at math and have been taking higher grade math courses but lately I've been bombing the math 12 (the senior math) course .. my math teacher says Calculus is easier than math 12, but my counselor says 1/3 of the students who take caluclus (regular, not AP) fail or drop the course (in my school)..</p>
<p>Whether or not calc is hard really depends on the student. I found it easy, but I'm quite good at math. If you've been breezing through most math classes, you'll probably be OK. What material is covered in the math 12 course you're having trouble in?</p>
<p>Oh, and as others have said, sine-integral is a special function, simply written as the antiderivative of sin(x)/x; there's no nice closed-form way to write it without the antiderivative. It's also denoted Si(x) sometimes.</p>
<p>Couldn't you solve that using integration by parts?</p>
<p>No. As Sly Si said, no closed-form expression exists for any antiderivatives of sin(x)/x. There are expressions that have infinitely many terms, however. </p>
<p>sin(x)/x is actually a really interesting function. If you like math, you might like this article:</p>
<p>trig seemed harder than calc.....perhaps alegbra 1 and 2 were even harder at the time...</p>
<p>I remember my teacher saying that you can't integrate sin (u) / (u).</p>
<p>If I had my TI89 with me, I'd use it.</p>