Common Integrals Flashcards by Liz O'Neill | Brainscape

Q

S dx

A

X+C

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Q

S 1/x dx

A

ln|x|+C

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Q

S kdx

A

kx+C

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Q

S x^-1 dx

A

ln|x|+C

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Q

S x^n dx

A

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

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Q

S x^-n dx

A

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

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Q

S e^n du

A

e^n+C

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Q

S lnu du

A

u*lnu-u+C

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Q

S u*e^n du

A

(u-1)*e^n+C

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Q

S 1/u*lnu du

A

ln|lnu|+C

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Q

S 1/a^2+u^2 du

A

1/a*arctan(u/a)+C

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Q

S 1/(u*rt(u^2-a^2) du

A

1/a*arcsec(u/a)+C

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Q

S arcsinu du

A

u*arcsinu+rt(1-u^2)+C

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Q

S arctanu du

A

uarctanu-1/2ln(1+u^2)+C

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Q

S arccosu du

A

u*arccosu-rt(1-u^2)+C

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Q

S 1/(ax+b) dx

A

1/a*ln|ax+b|+C

Q

S cosu du

A

sinu+C

Q

S secu*tanu du

A

secu+C

Q

S tanu du

A

ln|secu|+C

Q

S cscu du

A

ln|cacu-cotu|+C

Q

S sinu du

A

-cosu+C

Q

S cscu*cotu du

A

-cscu+C

Q

S sec^2u du

A

tanu+C

Q

S csc^2u du

A

-cotu+C

Q

S cotu du

A

ln|sinu|+C

Q

S sec^3 du

A

1/2(secutanuln|secu+tanu|+C

Q

S csc^3u du

A

1/2(-cscu*cotu+ln|cscu-cotu)+C