Integration Flashcards by Ben Stewart

Q

d/dx integral f(x) dx

A

f(x)

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Q

Integral dF(x)

A

F(x) + c

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Q

Integral cf(x) dx

A

c integral f(x) dx

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Q

integral (f(x) +/- g(x)) dx

A

Integral f(x) dx +/- integral g(x) dx

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Q

Integral between a and b f(x) dx

A

integral between b and a f(x) dx

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Q

Integral between a and a f(x) dx

A

0

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Q

Integral between a and b cf(x) dx

A

c integral between a and b f(x) dx

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Q

Integral between a and c f(x) dx + integral between c and b f(x) dx

A

Integral between a and b f(x) dx

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Q

Integral dx

A

x + C

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Q

Integral x^(n) dx

A

(x^(n+1))/(n+1) + C

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Q

Integral dx/x

A

ln |x| + C

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Q

Integral dx/(1 + x^2)

A

arctanx + C

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Q

Integral dx/(1-x^2)^1/2

A

arcsinx + c

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Q

Integral e^x dx

A

e^x + C

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Q

Integral a^x dx

A

a^x/ln(a) + C

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Q

Integral sinx dx

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A

cosx + C

Q

Integral cosx dx

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A

sinx + C

Q

Integral dx/(cos^(2)x)

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A

tanx + C

Q

Integral dx/(sin^(2)x)

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A

cotx + C

Q

Integral sinhx dx

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A

coshx + C

Q

Integral coshx

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A

sinhx + c

Q

Integral dx/(cosh^(2)x)

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A

tanhx + C

Q

Integral dx/(sinh^(2)x)

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A

cothx + C

Q

Integral dx/(1 - x^(2))

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A

1/2 ln|(1+x)/(1-x)| + C

Integral dx/(x^(2) +/- 1)^1/2

ln |x + (x^(2) +/- 1)| + C

Possible substitutions for (a^(2) - x^(2))^1/2

x = asinu or x = atanhu

Possible substitutions for (a^(2) + x^(2))^1/2

x = asinhu or x = atanu

Possible substitutions for (x^(2) - a^(2))^1/2

x = acoshu or x = a/cosu

Possible substitutions for trigonometric functions

u = tan(x/2) or u = sinx or u = cosx

Possible substitutions for hyperbolic functions

u = e^x or u = sinhx or u = coshx or u = tanh(x/2)