To integrate by parts u need to take 2 functions, in this case, you only have arctan(3x) and therefore you second function will just be 1. this sounds confusing but think about it:
arctan(3x) = 1*arctan(3x)
ill take
u = arctan(3x)
dv = 1
-so you know
du = 3/(1+9x^2) ...... derivative of tangent inverse
v = x
∫ u dv = uv - ∫ v du
∫ (arctan(3x) * 1) dx = x*arctan(3x) - ∫ (x * (3/(1+9x^2))) dx
= x*arctan(3x) - ∫ (3x / (1 + 9x^2)) dx
take w = 1 + 9x^2
dw = w' dx
dw = 18x dx
dx = dw / 18x
so now you have
= x*arctan(3x) - ∫ (3x)/w * dw/18x
the x's cancel and you end up with
= x*arctan(3x) - (1/6)*∫(1/w)dw
= x*arctan(3x) - (1/6) * ln|w|
= x*arctan(3x) - (ln(1 + 9x^2))/6.......1 + 9x^2 is always positive
your answer:
x*arctan(3x) - (ln(1 + 9x^2))/6
good luck
Answer:
if ya divide 13 by 356 u get 3.688202247191011
dat ya answer
:)
Answer:
i cant see it post again but closer up
Step-by-step explanation:
i cant see it
D) is correct
Length is 12, width is t less than length, so width is 12-t. Based on right triangle, 12^2 + (12-t)^2 = 32^2. So D is correct.
Answer:
7/12 ≈ 0.583
Step-by-step explanation:
See picture below. There are 21 totals higher than 6 out of 36 possible outcomes. The probability is therefore 21/36 = 7/12.