Inverse Trig Integrals
`int(-8)/(1+x^2)dx`
8arccot(x) or -8arctan(x) (both +c)
`y=sin^-1(2x+5)`
`dy/dx=1/sqrt(1-(2x+5)^2)*2`
`sin^-1(-.5)`
`-pi/6`
derive:
`y= 2^x`
`dy/dx=2^xln(2)`
`int_0^(1/2)(sin^(-1)x)/sqrt(1-x^2)dx`
`pi^2/72`
`y=arctan(cos(theta))`
`dy/(d theta)=(-sin(x))/(cos^2(x)+1`
`tan(arctan(10))`
`10`
`int (x^3+5x^2-32x-7)/(x-4)dx`
`x^3/3+9/2x^2+4x+9ln(abs(x-4))+c`
`int(1+x)/(1+x^2)dx`
`1/2ln(x^2+1)+tan^-1(x)+c`
`y=tan^-1(x^3)`
`dy/dx=(3x^2)/(1+x^6`
`sin(arctan(10))`
`(10sqrt(101))/101`
derive:
`y= 5^(x+1)`
`dy/dx=5^(x+1)ln(5)`
`int dx/(sqrt(x)*(1+x))`
`2tan^-1(sqrt(x)) +c`
`y=sin^-1(cos^-1(x))`
`1/sqrt(1-(cos^-1(x))^2)*-1/sqrt(1-x^2)`
`csc(cos^-1(3/5))`
`5/4`
`int(x/(x^4+2x^2+5))dx`
`1/4*tan^-1((x^2+1)/2)+c`