Integral Rules Sheet

Integral Rules Sheet - X 3 /3 + c: ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. E x + c : ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. A x /ln(a) + c : X 2 /2 + c: ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). Web symbolab integrals cheat sheet common integrals: X ln(x) − x + c:

E x + c : X ln(x) − x + c: ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. X 3 /3 + c: X 2 /2 + c: A x /ln(a) + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). Web symbolab integrals cheat sheet common integrals:

X 3 /3 + c: Web symbolab integrals cheat sheet common integrals: X ln(x) − x + c: ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. A x /ln(a) + c : E x + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). X 2 /2 + c: ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du.

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A x /ln(a) + c : Web symbolab integrals cheat sheet common integrals: X 3 /3 + c: E x + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥).

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X 3 /3 + c: Web symbolab integrals cheat sheet common integrals: E x + c : X 2 /2 + c: X ln(x) − x + c:

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X 3 /3 + c: ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). Web symbolab integrals cheat sheet common integrals: A x /ln(a) + c : E x + c :

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∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. X ln(x) − x + c: E x + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). A x /ln(a) + c :

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∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥.

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A x /ln(a) + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). X 3 /3 + c: X 2 /2 + c: X ln(x) − x + c:

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A x /ln(a) + c : X 3 /3 + c: ∫ f ( g ( x )) g ′ ( x ) dx = ∫ f ( u ) du. X ln(x) − x + c: Web symbolab integrals cheat sheet common integrals:

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A x /ln(a) + c : X 2 /2 + c: X 3 /3 + c: ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2 ∫ 𝑥 𝑥= 𝑥 ∫sin(𝑥) 𝑥=−cos(𝑥) ∫cos(𝑥) 𝑥=sin(𝑥). E x + c :

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X 3 /3 + c: X ln(x) − x + c: ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. A x /ln(a) + c : ∫𝑥−1 𝑥=ln(𝑥) ∫ 𝑥 𝑥 =ln(𝑥) ∫ |𝑥 𝑥=𝑥√𝑥 2 2.

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E x + c : Web symbolab integrals cheat sheet common integrals: X ln(x) − x + c: X 3 /3 + c: ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx.