Basic forms
Which substitution to use for int cos^2 xsin^3x dx
What is u=cos x
The expression x^2+2x+2 in the complete square form
What is
(x+1)^2+1
int cot^2 x dx=...
What is
-cot x-x+C
If integral contains \sqrt{a^2-x^2}, substitute x=...
What is
x=asin t
The types of partial fractions.
What is simple linear, repeated linear, simple irreducible quadratic, and repeated irreducible quadratic
Which substitution to use for int sec^4x tan^2x dx
What is
u=tan x
Complete the squares in
x^2-2x+3
What is
(x-1)^2+2
int tan^3x sec xdx=...
What is
\frac{1}{3}sec^3 x-sec x+C
If integral contains sqrt{x^2-a^2}, substitute x=...
What is
x=asec t
The partial fraction \frac{A}{x-r} is which type of partial fraction?
What is simple linear.
What algebraic method should be used to convert the fraction to basic integration form
int frac{1}{x^2+2x+2}dx
What is completing the squares in the denominator
Complete the squares in
2x^2+6x+7
What is
2(x+\frac{3}{2})^2+\frac{5}{2}
When the integral contains even powers of both sin x and
cos x , what trig identity formulas should be used?
What is half angle formulas.
int sqrt{x^2+1} dx will convert to this integral with a trig substitution.
What is
int sec^3 tdt
The partial fraction \frac{Ax+B}{ax^2+bx+c} belongs to this type of partial fraction
What is simple quadratic
The first thing to do when facing the integral of the expression
(x^2+2x-1)/(x+4)
What is polynomial long division
int\frac{1}{x^2+4x+5}dx=...
What is
tan^{-1}(x+2)+C
\int sin^2x cos^5xdx=...
What is
\frac{1}{5}sin x+\frac{1}{7}sin x+C
int \frac{sqrt{4-x^2}}{x^2}dx=...
What is
-\frac{sqrt{4-x^2}}{x}-sin^{-1}\frac{x}{2}+C
The general form of the partial fraction decomposition for
f(x)=\frac{3x+7}{x^3+x^2-2x}
is (without finding the coefficients of the decomposition)...
What is
frac{A}{x}+frac{B}{x+2}+\frac{C}{x-1}
Which substitution to use for the integral
int \frac{\sqrt{4x^2-1}}{x^2} dx
What is
2x=\sec t
or
x=\frac{1}{2}\sec t
int frac{5}{x^2-2x+10}dx=...
What is
\frac{5}{3}\tan^{-1}(\frac{1}{3}(x-1))+C
What is the hardest case for the integral
int tan^m x sec^n xdx
What is even
m
and odd
n
\int frac{1}{sqrt{x^2-1}}dx=...
What is
ln |x+sqrt{x^2-1}|+C
The general for of the partial fraction decomposition for the function (without finding the coefficients)
f(x)=\frac{7x^2-13x+13}{(x-2)(x^2-2x+3)}
What is
\frac{A}{x-2} + \frac{Bx+C}{x^2-2x+3}