CINT: Table of Integrals: Trigonometric forms

Question 1

∫tan u du

Accepted Answer

ln|sec u| + C

Question 2

∫cot u du

Accepted Answer

ln|sen u| + C

Question 3

∫sec u du

Accepted Answer

ln|sec u+tan u| + C

Question 4

∫csc u du

Accepted Answer

ln|csc u+cot u| + C

Question 5

∫tan³u du

Accepted Answer

½ tan²u + ln|cos u| + C

Question 6

∫cot³u du

Accepted Answer

−½ cot²u + ln|sen u| + C

Question 7

∫sec³u du

Accepted Answer

½ sec u tan u + ½ ln|sec u+tan u| + C

Question 8

∫csc³u du

Accepted Answer

−½ csc u cot u − ½ ln|csc u+cot u| + C

Question 9

∫sen²u du

Accepted Answer

½(u−sen u cos u) + C

Question 10

∫cos²u du

Accepted Answer

½(u+sen u cos u) + C

Question 11

∫sen³u du

Accepted Answer

−⅓(2−sen²u) cos u + C

Question 12

∫cos³u du

Accepted Answer

⅓(2−cos²u) sen u + C

Question 13

∫sen(au)cos(bu) du

Accepted Answer

[sin((a−b)u)/(2(a−b)) + sin((a+b)u)/(2(a+b))] + C

Question 14

∫cos(au)cos(bu) du

Accepted Answer

[sin((a−b)u)/(2(a−b)) + sin((a+b)u)/(2(a+b))] + C

Question 15

∫sen(au)sen(bu) du

Accepted Answer

[−cos((a−b)u)/(2(a−b)) + cos((a+b)u)/(2(a+b))] + C

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