Calculus: Integration, Differentiation, and Trigonometric Identities

integral of x^n

x^n+1/n+1

integral of 1/x

ln|x|

integral of e^x

e^x

integral of a^x

a^x/ln(a)

integral of cos (x)

sin(x)

integral of sin(x)

-cos(x)

integral of sec (x)

ln|sec(x)+tan(x)|

integral of csc (x)

-ln|csc(x)+cot(x)|

integral of tan (x)

ln|sec(x)|

integral of cot (x)

ln|sin(x)|

integral of sec^2 (x)

tan(x)

integral of csc^2(x)

-cot(x)

integral of sec(x)tan(x)

sec(x)

integral of csc(x)cot(x)

-csc(x)

integral of 1/√a^2-x^2

arcsin (x/a)

integral of 1/a^2-x^2

1/a * arctan(x/a)

integral of 1/x√x^2-a^2

1/a arcsec|x/a

derivative of sin (x)

cos(x)

derivative of cos (x)

-sin(x)

derivative of tan(x)

sec^2(x)

derivative of csc (x)

-csc(x)cot(x)

derivative of sec(x)

sec(x)tan(x)

derivative of cot(x)

-csc^2(x)

derivative of arcsin (x)

1/√a^2-x^2

derivative of arctan(x)

1/a^2-x^2

derivative of arcsec (x)

1/x√x^2-a^2

shell method

2pi* (integral from a to b) of shell radius*shell height

disc/washer method

pi* (integral from a to b) of R(x)^2-r(x)^2

arclength formula

(integral from a to b) √1+f'(x)^2

surface area formula

2pi* (integral from a to b) f(x) √1+f'(x)^2

sin^2(x) + cos^2(x) = 1

divide by sin - 1+cot^2(x)=csc^2(x)

divide by cos - tan^2(x)+1=sec^2(x)

cos(2x)

= cos^2(x)-sin^2(x)

sin(2x)

=2sin(x)cos(x)

cos^2(x)

= (1+cos(2x))/2

sin^2(x)

= (1-cos(2x))/2

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