Must Know Anti-Derivatives

∫ x^n dx

(1/(n+1))x^(n+1)+c

∫ cosx dx

sinx+c

∫ sec^2x dx

tanx+c

∫csc^2x dx

-cotx+c

∫ secxtanx dx

secx+c

∫sinx dx

-cosx+c

∫cscxcotx dx

-cscx+c

∫e^xdx

e^x+c

∫ 1/x dx

ln|x|+c

∫ tanx dx

-ln|cosx|+c

∫cotx dx

ln|sinx|+c

∫secxdx

ln|secx+tanx|+c

∫cscx dx

-ln|cscx+cotx|+c

∫f(x)/g(x) dx

could be u-sub, could be ln, could require division, could require multiplying by a form of one, could be other techniques we haven't learned yet, could be IMPOSSIBLE!!

∫f(x)g(x) dx

could be a pre-memorized, could be u-sub, could require multiplying it out, could be other techniques we haven't learned yet, could be IMPOSSIBLE!!

d/dx(∫f(t)dt)

f(x), depending on the upper and lower x-values of integration. It might be more complicated due to the chain rule. But still... it's fundamental!

∫f'(x)dx

f(x) + c. It's fundamental!

∫f(x)dx

F(x) + c, where the derivative of F is f. It's fundamental!

∫f(x)dx, from x=a to x=b

F(b) - F(a), where the derivative of F is f. It's fundamental (and saves us 18 minutes)!

∫ du/sqrt(a^2 - u^2)

arcsin(u/a) + c

∫ du/(a^2 + u^2)

(1/a)arctan(u/a) + c