Inverse Trig & L'Hopital
(d/dx) (arctan (x))
what is 1/(1+x2)
The integration by parts formula
what is ∫u dv=uv−∫v du
∫sin(x)cos(x)dx
u=sin x
what is 1/2 sin2(x)+C
the trig sub typically used for Sqrt{a2-x2}
what is x=a sin(θ)
Usually the first thing you should check before integrating a rational function
what is whether the degree of the numerator is greater than or equal to the denominator.
If so, use long division first.
lim x->0 [(sin (x))/x]
What is 1
∫xexdx
u=x, dv=exdx
what is xex-ex+c
∫tan(x)dx
u=cos x
what is ln|sec(x)|+C
decompose 5/[x(x+2)]
what is [5/(2x)]−{5/[2(x+2)]}
∫1infinity 1/(x2)dx
what is 1; the integral converges
Lim x->infinity [Ln(x)/x]
what is 0
∫ln(x)dx
what is xln(x)-x+C
∫sin3(x)cos2(x)dx
what is -(1/3)cos3(x)+(1/5)cos5(x)+C
∫dx/{sqrt[9-x2]}
what is arcsin(x/3)+C
converge or diverge: ∫1infinity 1/x dx
what is the integral diverges
∫1/[sqrt{1-x2}]dx
what is arcsin(x)+C
∫xcos(x)dx
what is xsin(x)+cos(x)+C
u=x, dv=cos(x)dx
∫sec3(x)dx
what is (1/2)sec(x)tan(x)+(1/2)ln|sec(x)+tan(x)|+C
∫1/(x2-1)dx
what is (1/2)ln|x-1|-(1/2)ln|x+1|+C
The integration strategy most appropriate for
∫x sqrt{x+1} dx
what is u-sub u=x+1
lim x->0 [(ex-1-x)/x2]
what is 1/2
∫x2exdx
what is ex(x2-2x+2)+C
u=x2 , dv=exdx
∫sin2(x)dx
what is (x/2)-[sin(2x)/4]+C
∫x2/(x2+4) dx
what is x-2arctan(x/2)+C
∫0infinity e-xdx
what is 1; the integral converges