How do you solve integrals, guys? any good webpages?

>>276585

Always first looking if partial itegration may help. Then if partial integration with 1 as u', then if when derivating it cycles- if that means several times partial integration until last integral = starting integral on the left side, so can be put on the left side.
Only then substitution.
If the integrand is a rational function a partial fraction decomposition is needed to split into several simpler integrals.

For websites the gold standard is wolframalpha but unless you have pro you cannot see the solution, only the result.
Not as powerful but still able to solve quite a few types of integrals with solution is the symbolab calculator.

File: calc.png (1KB, 139x63px) Image search: [Google]

1KB, 139x63px

Since this is a thread pertaining to calc I'll bump with my brainlet question

It's not really that I don't understand how to do it, but I'm a bit confused on the concept. I've divided the whole thing by x^2 and now I need to determine the limit of the numerator (5-9x^2). I don't understand why the limit of that is negative infinity?

also, dunno, might help you OP

http://www.integral-calculator.com/

>>276701
Here's a quick tip, friendo. When evaluating limits that run off to inf/-inf, and the equation you're taking the limit for is simple (eg. a fraction consisting of two polynomials), you can usually determine the limit just by looking at the highest degree exponent. For your picture's case, the highest exponent is that -9x^4. That means your numerator is changing faster than your denominator and since it is heading to infinity, it becomes irrelevant. That limit may as well be lim x->inf of (-x), which equates to negative inf.
Now if the highest degree of an exponent was in the denominator, you can infer that the denominator is changing faster than the numerator. If you think about the denominator getting bigger and bigger, it's clear that the fraction itself is getting smaller and smaller. In fact, if the highest degree of an exponent is in the denominator, the limit of that fraction is 0.
For the last case, if the degree of the highest exponent is the same for both the numerator and the denominator (eg. (3x^5)/(2x^5 + 3)) then the limit is simply the coefficients of the highest degree exponent (eg. 3/2).

In case you didn't really feel like reading that block of text, the answer to why the limit of (5-9x^2) as it approaches infinity = -infinity is because there is a negative being applied to the variable you are taking the limit of.

>>276585
There are many techniques to deal with specific cases you pick up as you learn integrals. In any case, probably try khanacademy.