I'm going to talk about antiderivatives. An antiderivative is a general solution, while an integral is more specific and you must solved for c (the constant). Second, an antiderivative is just a backwards derivative. Your given is F' or F'' and you must find F.
Third, how to find an antiderivative: if you're given ax^b, where a is your constant, x is your variable and b is your exponent, your formula is (a/(b+1))(x^(b+1))
*when solving for the antiderivative, always add "+c" in place of a constant
**when solving for an integral, you will be given something like f(1)=2, in that case, you plug 1 in for x in your antiderivative and set it equal to 2 and solve to find the constant.
***When given the second derivative, just take the antiderivative twice.
****When given an integral, it is always used with the integral symbol (a large S) before and dx after.
*****Shortcut: if you have a fractional exponent, add one and multiply the coefficient by the reciprocal.
******Trig Functions: you just do the opposite of the derivative.
Ex 1. S dx =x+c
Ex 2. S (x+2)dx = (1/1+1)(x^1+1)=x^2/2+2x+c
Ex 3. S (3x^4-5x^2+x)dx =3x^5/5-5x^3/3+x^2/2+c
Ex 4. S sinxdx = -cosx
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