Inverse Trig Integrals
Inverse Trig Derivatives
Inverse Trig Expressions
Derivatives/Algebra
100

`int(-8)/(1+x^2)dx`

8arccot(x)  or -8arctan(x) (both +c)

100

`y=sin^-1(2x+5)`

`dy/dx=1/sqrt(1-(2x+5)^2)*2`

100

`sin^-1(-.5)`

`-pi/6`

100

derive: 

`y= 2^x`

`dy/dx=2^xln(2)`

200

`int_0^(1/2)(sin^(-1)x)/sqrt(1-x^2)dx`

`pi^2/72`

200

`y=arctan(cos(theta))`

`dy/(d theta)=(-sin(x))/(cos^2(x)+1`

200

`tan(arctan(10))`

`10`

200

`int (x^3+5x^2-32x-7)/(x-4)dx`

`x^3/3+9/2x^2+4x+9ln(abs(x-4))+c`

300

`int(1+x)/(1+x^2)dx`

`1/2ln(x^2+1)+tan^-1(x)+c`

300

`y=tan^-1(x^3)`

`dy/dx=(3x^2)/(1+x^6`

300

`sin(arctan(10))`

`(10sqrt(101))/101`

300

derive: 

`y= 5^(x+1)`

`dy/dx=5^(x+1)ln(5)`

400

`int dx/(sqrt(x)*(1+x))`

`2tan^-1(sqrt(x)) +c`

400

`y=sin^-1(cos^-1(x))`

`1/sqrt(1-(cos^-1(x))^2)*-1/sqrt(1-x^2)`

400

`csc(cos^-1(3/5))`

`5/4`

400

`int(x/(x^4+2x^2+5))dx`

`1/4*tan^-1((x^2+1)/2)+c`