Integration Flashcards by EV EV | Brainscape

Q

∫ Cosx

A

Sinx

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Q

∫ x^n

A

x^n+1/n+1

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Q

∫ Sec²x

A

tanx

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Q

∫ Secx Tanx

A

Secx

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Q

∫ Cosecx Cotx

A

–Cosecx

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Q

∫ Cosec²x

A

-Cotx

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Q

∫ 1/x

A

log|x|

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Q

∫ k

A

kx

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Q

∫ e^x

A

e^x

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Q

∫ 1/√(1-x²)

A

Sin-¹x
-Cos-¹x

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Q

∫1/1+x²

A

tan-¹x
-Cot-¹x

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Q

∫ 1/|x|√(x²-1)

A

Sec-¹x
-Cosec-¹x

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Q

∫ a^(x)

A

a^(x)/log|x|

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Q

∫ tanx

A

Log|Secx|

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Q

∫ Cotx

A

log|Sinx|

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Q

∫ Secx

A

log|Secx+Tanx|

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Q

∫ Cosecx

A

log|cosecx - cotx|

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Q

∫ 1/x² - a²

A

1/2a |x-a/x+a|

Q

∫ 1/√x²-a²

A

log|x+√(x²-a²)|

Q

∫1/x²+a²

A

1/a tan-¹(x/a)

Q

∫ 1/√(a²+x²)

A

Log|x+√(x²+a²)|

Q

∫1/(a²-x²)

A

1/2a log|a+x/a-x|

Q

∫ 1/√a²-x²

A

Sin-¹(x/a)

Q

∫ (px+q)/(x-a)(x-b)

A

A/(x-a) + B/(x-b)

Q

∫ px+q/(x-a)²

A

A/(x-a) + B/(x-a)²

Q

(px²+qx+r)/(x-a)(x-b)(x-c)

A

A/(x-a) + B/(x-b) + C/(x-c)

Q

(px²+qx+r)/(x-a)²(x-b)

A

A/(x-a) + B/(x-a)² + C/(x-b)

Q

(px²+qx+r)/(x-a)(x²+bx+c)

A

A/(x-a) + Bx+C/(x²+bx+c)

Q

∫f(x)g(x)dx

A

F(x) ∫g(x) dx - ∫ [ df(x)/dx ] ∫ g(x) dx

Q

√x²–a²

A

x/2 √(x²-a²) - a²/2 log |x+√x²-a²|

Q

∫ √x²+a² dx

A

x/2 √x²+a² +a²/2 log |x+√x²+a²|

Q

∫ √a²-x² dx

A

x/2 √a²-x² + a²/2 Sin-¹ (x/a)

Q

Integration by parts priority order

A

ILATE

Q

∫eˣ [f(x)+f’(x)] dx

A

eˣf(x)

Q

P₀ ₐ∫ᵇ f(x)dx

A

ₐ∫ᵇ f(t) dt

Q

P₁ ₐ∫ᵇ f(x)dx

A

–ᵦ∫ᵃf(x)dx

Q

P₂ ₐ∫ᵇ f(x) dx

A

ₐ∫ᶜ f(x)dx + ꜀∫ᵇ f(x)dx

Q

P₃ ₐ∫ᵇ f(x)dx

A

ₐ∫ᵇ f(a+b-x)dx

Q

P₄ ₀∫ᵃf(x)dx

A

₀∫ᵃf(a-x)dx

Q

P₅ ₀∫²ᵃ f(x)dx

A

₀∫ᵃ f(x)dx + ₀∫ᵃf(2a-x)dx

Q

P₆ ₀∫²ᵃ f(x)dx

A

2₀∫ᵃf(x)dx If (2a-x) = f(x)
0 If (2a-x) = -f(x)

Q

P₇ ₋ₐ∫ᵃ f(x)dx

A

2₀∫ᵃf(x)dx If f(-x)=f(x)
0 If f(-x)=-f(x)

Q

P₈ ₐ∫ᵇ f(x)/f(x)+g(x)

A

b-a/2 If g(x)=f(a+b-x)