Inverse Trig Integrals (and others)

Inverse Trig Integrals

100

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

8arccot(x)  or -8arctan(x) (both +c)

200

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

pi^2/72

300

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

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

400

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

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

Inverse Trig Derivatives

100

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

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

200

y=arctan(cos(theta))

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

300

y=tan^-1(x^3)

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

400

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

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

Inverse Trig Expressions

100

sin^-1(-.5)

-pi/6

200

tan(arctan(10))

10

300

sin(arctan(10))

(10sqrt(101))/101

400

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

5/4

Derivatives/Algebra

100

derive: 

y= 2^x

dy/dx=2^xln(2)

200

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

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

300

derive: 

y= 5^(x+1)

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

400

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

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