If derivatives are the Justice League of calculus, indefinite integrals are the Anti-Justice League. Indefinite integrals are the antithesis of derivatives—they represent the exact opposite operation. The term antiderivative means the same thing as an indefinite integral...it's like they're Two-Face/Harvey Dent.
It's important to point out the difference between definite and indefinite integrals. Since definite integrals represent an area, they give an actual number. Indefinite integrals, on the other hand, are infinite collections of functions. If the infinite part makes you feel like Superman + Kryptonite, all we're talking about is the + C that gets added to the end of the antiderivative. The constant C can be any number, so there are infinitely many choices. Read on to see what we mean, and you'll feel super once again.
Integration Made Easy:
The only way it'd be easier is if you could walk up to the integrand and just ask, "Whose derivative are you?" It'd make for a good photo op, too.
Methods of Integration:
This is a cookbook of techniques used to solve more difficult integrals. If you tried to make hot tomato soup in a blender last night, this link won't be able to help your cooking skills.
Drill Sheet of Improper Integrals:
There's nothing taboo about improper integrals. This sheet will show you how to tackle them. You'll be so good your fans will rush the field when you're finished.
Integration by u-Substitution:
Not you-substitution, but it'd work as well if you replaced the integration variable with a picture of yourself. This link demonstrates the simplest of the integration tricks.
Integration by Trigonometric Substitution:
You can either lay your head on a pillow at night, or you can use it in a pillow fight with your roommate. Likewise, you can use sine, cosine, and tangent for more than just trigonometry. Learn how to use them to solve integrals.
Integration by Parts:
When you were young, your mom probably yelled at you when you took the dishwasher apart and couldn't put it back together. Don't worry. Integration by parts isn't nearly as messy.
Integration by Partial Fractions:
The idea of partial fractions sounds something like seeing a pair of legs walking around without a torso or head. Learn how to use the method of partial fractions to solve integrals.
Improper Integrals, Convergence and Divergence:
Some improper integrals are well behaved. Others are deviants. You'll learn how to distinguish between the angels and the devils in this video.
Table of Integrals:
Don't be fooled. Every scientist and engineer uses a table of integrals when they need to solve a tough problem. Here's a link to a table of the most common integrals and a few freaks.
Indefinite Integral Calculator:
It's your birthday. Have your cake and eat it, too. Check your work with this indefinite integral calculator.