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Level 575

Integrations


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§sin(x)dx
-cos(x) +C
§cos(x)dx
Sin(x) + C
§tan(u)du
Ln|sec(u)| + C
§cot(u)du
Ln|sin(u)| + C
§sec(u)du
Ln|sec(u) + tan(u)| +C
§csc(u)du
Ln|csc(u) - cot(u)| + C
§e^u du
e^u + C
Dx(e^u)
e^u Dx(u)
Exp(x)
e^x
ln(e)
1, when x is 0 or 1
e
Exp(1)
§a^u du
1/ln(a) • a^u + C
Dx(a^u)
a^u • ln(a) • Dx(u)
Loga (x)
lnx/lna
Dx(loga (u) )
1/u • loga (e) • Dx(u)
a^x
e^xlna
Dx(sin^-1 (u))
[1/sq rt (1-u^2) ] • dx(u)
Dx(cos^-1 (u))
-[1/ sq rt (1-u^2)] • dx(u)
Dx(tan^-1 (u))
1/(1+u^2) • dx(u)
Dx(cot^-1 (u))
- 1/(1+ u^2) • dx(u)
Dx(sec^-1 (u))
1/(u•sq rt (u^2 - 1)) • dx(u)
Dx(csc^-1 (u))
- 1/(u•sq rt (u^2 - 1)) • dx(u)
Sin^-1 (u/a) +C
§ 1/ sq rt (a^2 - u^2) du
(1/a) Tan^-1 (u/a) + C
§ 1/ (a^2 + u^2) du
(1/a) sec^-1 (u/a) + C
§ 1/ u • sq rt(u^2 - a^2) du
Integration
Reverse differentiation
Indefinite Integration
The general solution.
Definite Integration
The particular solution.
Negative Area
The area is beneath the x axis as opposed to above.
Area Between Curves
found by integration two lines
Top Graph-Bottom Graph
The way to remember the order to write the two equations before simplifying and integrating.
∫adx
ax+C
∫xⁿdx
(xⁿ⁺¹)/(n+1)+C
∫(1/x)dx
ln|x|+C
∫(e^x)dx
e^x+C
∫(a^x)dx
a^x/lna+C
∫lnxdx
xlnx-x+C
∫sinxdx
-cosx+C
∫cosxdx
sinx+C
∫tanxdx
ln|secx|+C
∫sec²dx
tanx+C
∫secxtanxdx
secx+C
∫csc²x dx
-cotx+C
∫cscxcotxdx
-cscx+C
∫dx/(a²+x²)
1/aArctan(x/a)+C
∫dx/(√(a²-x²)
Arcsin(x/a)+C
∫ cosx dx
sinx + C
∫ sinx dx
-cosx + C
∫ sec²x dx
tanx + C
-cscx + C
∫ cscx cotx dx
secx + C
∫ secx tanx dx
∫ csc²x dx
-cotx + C