Trig Integrals and Derivatives

Trig integrals for Cal II Test 2 (also includes derivatives and integrals of exponential functions)

∫ tanx dx = ?

-ln|cosx| + C

∫ secx dx = ?

ln|secx+tanx| + C

∫ cscx dx = ?

-ln|cscx+cotx| + C

∫ cotx dx = ?

-ln|cscx| + C

How would you write the antiderivative of the expression in the following image?

How would you write the antiderivative of the expression in the following image?

How would you write the antiderivative of the expression in the following image? (Where u replaces the variable x)

dy/dx cotx = ?

-csc²x

dy/dx cscx = ?

-cscxcotx

dy/dx a^{x} = ?

a^{x}\ln\left(a\right)

\int e^{ax+b}  = ?

\frac{1}{a}e^{ax+b}+C

\int ae^{ax} = ?

e^{ax}+C