calculus: integral Flashcards

1
Q

∫kf(u)du

A

k∫f(u)du

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2
Q

∫du

A

u+c

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3
Q

∫kdu

A

ku + c

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4
Q

∫[f(u) +- g(u)]du

A

∫f(u)du +- ∫g(u)du

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5
Q

∫u^ndu

A

u(n+1)/(n+1) + C

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6
Q

∫du/n

A

ln|u| + C

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7
Q

∫e^udu

A

e^u + c

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8
Q

∫sinudu

A

-cosu + c

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9
Q

∫cosudu

A

sinu + c

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10
Q

∫tanudu

A

-ln|cosu| + C

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11
Q

∫cscudu

A

-ln|cscu + cotu| + c

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12
Q

∫secudu

A

ln|secu + tanu| + C

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13
Q

∫cotudu

A

ln|sinu| + C

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14
Q

∫sec^2udu

A

tanu + C

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15
Q

∫csc^2udu

A

-cotu + C

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16
Q

∫secutanudu

A

secu + c

17
Q

∫cscucotudu

A

-cscu + c

18
Q

∫du/square root(a^2 -u^2)

A

arcsin(u/a) + c

19
Q

∫du/(a^2+u^2)

A

1/a(arctan(u/a)) + c

20
Q

∫du/ u*square root(a^2-u^2)

A

1/a(arcsec(|u|/a) + c