Intergral cheet sheet

What is the integral of dx?

x + C

What is the integral of x^n dx, where n ≠ -1?

(x^{n+1)/(n+1) + C

What is the integral of e^x dx?

e^x + C

What is the integral of a^x dx?

(a^x)/ln a + C

What is the integral of x^{-1} dx?

ln|x| + C

What is the integral of e^{ax} dx?

1/a e^{ax} + C

What is the integral of cos x dx?

sin x + C

What is the integral of sin x dx?

-cos x + C

What is the integral of sec x tan x dx?

sec x + C

What is the integral of csc x cot x dx?

-csc x + C

What is the integral of sec^2 x dx?

tan x + C

What is the integral of csc^2 x dx?

-cot x + C

What is the integral of {dx}/{x^2 + a^2}?

1/a tan^{-1}(x/a) + C

What is the integral of {x dx}/{x^2 + a^2}?

1/2 ln|x^2 + a^2| + C

What is the integral of tan x dx?

ln|sec x| + C

What is the integral of cot x dx?

ln|sin x| + C

What is the integral of sec x dx?

ln|sec x + tan x| + C

What is the integral of csc x dx?

ln|csc x - cot x| + C