Standard Integrals (ax + b) Flashcards by Gordian Leo | Brainscape

Q

INTEGRATE

xⁿ

A

(1/n+1) * x⁽ⁿ⁺¹⁾ + C

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Q

INTEGRATE

e^x

A

e^x +C

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Q

INTEGRATE

1 / x

A

ln | x | + C

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Q

INTEGRATE

sin x

A

cos x + C

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Q

INTEGRATE

cos x

A

sin x + C

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Q

INTEGRATE

sec² x

A

tan x + C

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Q

INTEGRATE

1 / √(1 - x²)

A

sin^-1 x + C

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Q

INTEGRATE

1 / √(1 - x²)

A

cos^-1 x + C

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Q

INTEGRATE

1 / (1 + x²)

A

tan^-1 x + C

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Q

INTEGRATE

tan x

A

ln (cos x) + C

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Q

INTEGRATE

sinh x

A

cosh x + C

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Q

INTEGRATE

cosh x

A

sinh x + C

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Q

INTEGRATE

sech² x

A

tanh x + C

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Q

INTEGRATE

1 / √(1 + x²)

A

sinh^-1 x + C

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Q

INTEGRATE

1 / √( -1 + x² )

A

cosh^-1 x + C

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Q

INTEGRATE

1 / ( 1 - x²)

A

tanh^-1x + C

Q

For Standard Integrals,

a, b, C and n =/= -1 are … .

A

constants

Q

INTEGRATE

(ax + b)ⁿ

A

1/a * 1/(n+1) * (ax + b)ⁿ⁺¹ + C

Q

INTEGRATE

e^{(<em>ax + b</em>)}

A

1/a * e^{(<em>ax + b</em>)}+ C

Q

INTEGRATE

1 / (ax + b)

A

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

Q

INTEGRATE

sin (ax + b)

A

-1/a cos(ax + b) + C

Q

INTEGRATE

cos (ax + b)

A

1/a sin(ax + b) + C

Q

INTEGRATE

sec² (ax + b)

A

1/a tan(ax + b) + C

Q

INTEGRATE

1 / √(1 - (ax + b)² )

A

1/a sin^-1 (ax + b) + C

Q

INTEGRATE

1 / √(1 - (ax + b)²)

A

1/a cos^-1 (ax + b) + C

Q

INTEGRATE

1 / (1 + (ax + b)²)

A

1/a tan^-1(ax + b) + C

Q

INTEGRATE

tan (ax + b)

A

-1/a ln( cos(ax+b) ) + C

Q

INTEGRATE

sinh (ax + b)

A

1/a cosh (ax + b) + C

Q

INTEGRATE

cosh (ax + b)

A

1/a sinh (ax + b) + C

Q

INTEGRATE

sech² (ax + b)

A

1/a tanh (ax + b) + C

Q

INTEGRATE

1 / √(1 + (ax + b)²)

A

1/a sinh^-1 (ax + b) + C

Q

INTEGRATE

1 / √(-1 + (ax + b)2)

A

1/a cosh^-1 (ax + b) + C

Q

INTEGRATE

1 / (1 - (ax + b)²)

A

1/a tanh^-1(ax + b) + C