Basic integration formulas PDF

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Math 107 Basic Integration Formulas For the Gateway exam and in-class quizzes and mid-term exams, you will need to remember some very basic integration formulas (you will not be able to take in any notes or tables of integrals etc). The formulas that you need to remember are listed below. In addition to the various techniques we have covered in class, these are the formulas you should know for exams. R n+1 1. xn dx = xn+1 + C if n 6= −1 R 2. 1x dx = ℓn|x| + C R 3. ex dx = ex + C R 4. cos(x) dx = sin(x) + C R 5. sin(x) dx = − cos(x) + C R 1 R 1 1 6. 1+x arctan( ax ) + C . 2 dx = arctan(x) + C, and its general version a2 +x2 dx = a R R 1 dx = arcsin(x) + C, and its general version √ 21 2 dx = arcsin( xa ) + C . 7. √1−x 2 a −x R 1 8. cos2 (x) dx = tan(x) + C 9.

R

1 sin2 (x)

cos(x)

dx = − sin(x) + C

You also need to remember the basic trig identity 10. sin2 (x) + cos2 (x) = 1

(Equivalently, sec2 (x) = 1 + tan2 (x))

You may also find the double-angle formulas useful for reducing powers of sin(x) and cos(x). They will be provided if they are required, but if you know them and want to use them at other times, you may. They are: 11. sin(2θ) = 2 sin(θ) cos(θ ) 12. cos(2θ) = 2 cos2 (θ) − 1 = 1 − 2 sin2 (θ). Rewritten, this says (a) cos2 (θ) = 21 (cos(2θ) + 1). (b) sin2 (θ) = 12 (1 − cos(2θ)). 13. Rules of natural logarithms ln(AB) = ln(A) + ln(B),

ln(

A ) = ln(A) − ln(B), B

ln Ap = p ln A

NOTE: Your book does not mention the secant, cosecant, and cotangent functions. If you are sin(x) 1 and tan(x) = cos(x) familiar with these, since sec(x) = cos(x) , Integral 8 may be written as Z sec2 (x) dx = tan(x) + C and since csc(x) =

1 sin(x)

x) , Integral 9 may be written as and cot(x) = cos( sin(x) Z csc2 (x) dx = cot(x) + C...