Integral Cheat Sheet - ′= −∫ ′ ∫integral of a constant: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: © 2005 paul dawkins integrals definitions definite integral: ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule:
Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. © 2005 paul dawkins integrals definitions definite integral: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ′= −∫ ′ ∫integral of a constant: ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out:
( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: ′= −∫ ′ ∫integral of a constant: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: © 2005 paul dawkins integrals definitions definite integral: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥
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Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. ′= −∫ ′ ∫integral of a constant: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: © 2005 paul dawkins integrals definitions definite integral: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥
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⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ′= −∫ ′ ∫integral of a constant: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite.
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Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: ′= −∫ ′ ∫integral of a constant: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: © 2005 paul dawkins integrals definitions definite integral:
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′= −∫ ′ ∫integral of a constant: © 2005 paul dawkins integrals definitions definite integral: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out:
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⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: ′= −∫ ′ ∫integral of a constant: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. © 2005 paul dawkins integrals definitions definite integral:
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′= −∫ ′ ∫integral of a constant: ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: © 2005 paul dawkins integrals definitions definite integral: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule:
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( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 © 2005 paul dawkins integrals definitions definite integral: ′= −∫ ′ ∫integral of a constant:
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( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: ′= −∫ ′ ∫integral of a constant: ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: © 2005 paul dawkins integrals definitions definite integral: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥
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( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: ′= −∫ ′ ∫integral of a constant: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. © 2005 paul dawkins integrals definitions definite integral:
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⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ( ) 𝑥=𝑥⋅ ( ) ∫taking a constant out: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite. ′= −∫ ′ ∫integral of a constant:
( ) 𝑥=𝑥⋅ ( ) ∫Taking A Constant Out:
(𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥 ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫sum/difference rule: ′= −∫ ′ ∫integral of a constant: Integral substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) definite integrals rules definite.