Indefinite Integrals Help

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The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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Indefinite Integrals Help

A function `F(x)` is called an integral or antiderivative of a function `f(x)`, if `F'(x)=f(x)` for all `x` in the domain of `f`. There are an infinite number antiderivatives for any given function, as shown below. This is why it is referred to as an indefinite integral.

If:  `F(x)=3x^2+2,   F'(x)=6x`
If:  `F(x)=3x^2+8,   F'(x)=6x`
If:  `F(x)=3x^2-6,   F'(x)=6x`
     `vdots`
If:  `F(x)=3x^2+C,   F'(x)=6x`,    Where `C` is any constant.`

The symbol for an integral or antiderivative is `int`.

The integral of a function is the reverse of differentiation. It is the function that has a derivative that is equal to what is shown immediately after the integral symbol.

From above: `int 6x dx = F(x)+C`. therefore: `int f(x) dx = F(x)+C`.

Listed below are a number of basic integral formulas derived from their corresponding derivative formulas. Others will follow as we learn more advanced techniques of integration.

`int kf(x)dx = kint f(x)dx`
`int e^xdx=e^x+C`

`int [f(x)+-g(x)]dx = int f(x)dx+-int g(x)dx`
`int` `a^xdx=a^x/(ln(a))+C, a>0, ane1`

`int kdx = kx+C`
`int` `dx/x=ln|x|+C`

`int` `x^ndx=x^(n+1)/(n+1)+C, n ne-1`
`int tan(x)dx=-ln|cos(x)|+C`

`int sin(x)dx=-cos(x)+C`
`int cot(x)dx=ln|sin(x)|+C`

`int cos(x)dx=sin(x)+C`
`int sec(x)dx=ln|sec(x)+tan(x)|+C`

`int sec^2(x)dx=tan(x)+C`
`int csc(x)dx=-ln|csc(x)+cot(x)|+C`

`int csc^2(x)dx=-cot(x)+C`
`int` `dx/sqrt(a^2-x^2)=sin^(-1)(x/a)+C`

`int sec(x)tan(x)dx=sec(x)+C`
`int` `dx/sqrt(a^2+x^2)=1/a*tan^(-1)(x/a)+C`

`int csc(x)cot(x)dx=-csc(x)+C` `int` `dx/(xsqrt(x^2-a^2))=1/a*sec^(-1)(x/a)+C`