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Integration Chart - (5) ∫(x + a)ndx = (x + a)n + 1 n + 1, n ≠ − 1. ∫ e u d u = e u + c. Web ©2005 be shapiro page 3 this document may not be reproduced, posted or published without permission. ∫ cos u d u = sin u + c. (6) ∫x(x + a)ndx = (x + a)n + 1((n + 1)x − a) (n + 1)(n + 2) (7) ∫ 1 1 + x2dx = tan − 1x C dx = cx + c. ∫ csc u cot u d u = −csc u + c. (1) ∫1 xdx = ln |x|. ∫ xdx = + c. ∫ 1 dx = arcsin x + c −.

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(1) ∫1 xdx = ln |x|. ∫ cos u d u = sin u + c. Integrals that are logarithmic functions. Web ©2005 be shapiro page 3 this document may not be reproduced, posted or published without permission. ∫ csc u cot u d u = −csc u + c.

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∫ sin u d u = −cos u + c. ∫ csc 2 u d u = −cot u + c. ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. 2 x x ∫ xdx = +.

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∫ d u u = ln | u | + c. (4) integrals of rational functions. Integrals that are logarithmic functions. Integrals of rational and irrational functions. C dx = cx + c.

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Web integrals with trigonometric functions z sinaxdx= 1 a cosax (63) z sin2 axdx= x 2 sin2ax 4a (64) z sinn axdx= 1 a cosax 2f 1 1 2; ∫ cos u d u = sin u + c. 2 x x ∫ xdx = + c. Web ©2005 be shapiro page 3 this document may not be reproduced, posted.

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C dx = cx + c. Web table of basic integrals. 2 x x ∫ xdx = + c. ∫ e u d u = e u + c. ∫ sec 2 u d u = tan u + c.

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∫xndx = 1 n + 1xn + 1, n ≠ − 1. ∫ sec u tan u d u = sec u + c. ∫ f ( x ) g ′ ( x ) dx = f ( x ) g ( x ) − ∫ g ( x ) f ′ ( x ) dx. ∫ csc 2 u.

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∫ csc u cot u d u = −csc u + c. ∫ a x d x = a x ln ( a) + c. ∫ 1 x d x = ln | x | + c. 2 x dx = c. ∫ e x d x = e x + c.

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∫ e u d u = e u + c. The definite integral of a function gives us the area under the curve of that function. Web table of basic integrals. ∫ dx = ln x + c. ∫ a x d x = a x ln ( a) + c.

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Want to learn more about integrating exponential functions and 1 x ? Web table of basic integrals. ∫ 1 dx = arcsin x + c −. 2 x x ∫ xdx = + c. ∫ 1 x d x = ln | x | + c.

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∫ 1 (x + a)2dx = − 1 x + a. ∫ = arctan x + c. ∫ csc 2 u d u = −cot u + c. ∫ a u d u = a u ln a + c. Web ©2005 be shapiro page 3 this document may not be reproduced, posted or published without permission.

∫ 1 (X + A)2Dx = − 1 X + A.

Web table of basic integrals. Want to learn more about integrating exponential functions and 1 x ? Web integrals with trigonometric functions z sinaxdx= 1 a cosax (63) z sin2 axdx= x 2 sin2ax 4a (64) z sinn axdx= 1 a cosax 2f 1 1 2; (2) ∫udv = uv − ∫vdu.