Calculus 2 exam 3
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What is
1/x
^{2}+1 dx?
Inverse tangent rule: tan^{1}x+c

What is a trig identity for sin2x?
Sin2x=2sinxcosx

What is a trig identity for cos^{2}x?
Cos^{2}x=(1+cos2x)/2

What is a trig identity for sin^{2}x?
sin^{2}x=(1cos2x)/2

what is the antiderivative of 1/u?
1/u= lnu+c

what is the anitderivative of sec(u) du?
sec(u)du = lnsec(u)+tan(u)+c

What is the formula for integration by parts?
u dv = uvvdu

what does ILATE stand for and what is it used for?
 I= inverse
 L= logarithm
 A= algebraic
 T= trig functions
 E= Exponentials
 *used to choose what "u" should be in integration by parts.

what is
secx dx?
sec(x) dx = lnsec(x)+tan(x)+c

u
^{2}a
^{2}/u
^{2} du equals?
=
u^{2}a^{2}/u^{ }+ lnu+u^{2}a^{2}+c

cos
^{1}udu equals?
=
ucos1u(1u2)^{ }+c

what is
du/u
(u
^{2}a
^{2}) ?
=1/a sec^{1} u/a +c

How do you complete the square?
(ax^{2}+bx+c) = (ax^{2}+bx+(b/2)^{2}) (b/2)^{2}+c

what is
1/
(a
^{2}u
^{2}) du?
= sin^{1}(u/a)+c

What is
sin
^{2}(x)dx?
= x/2  sin(2x)/4 +c

what is
cos
^{2}(x)dx ?
= x/2 + sin(2x)/4 +c

u
^{2} ln(u) du ?
= u^{n+1 }/ (n+1)^{2 }[(n+1)ln(u)1] +c

what is the derivative of 1/(x^{2}+1)?
= tan^{1}x+c

(a
^{2}+u
^{2})/ u
^{2 }du?
=
 (a^{2}+u^{2})/u + ln(u+(a^{2}+u^{2})) +c

what do you do when the top is longer than the bottom on the integral of polynomials?
long divide the bottom from the top first.