Evaluate the following integral cotx dx Select one: x cot""x -In(1+x?)+c 2 x cot-1x +2/1+x² + C х cot 1x - Im/ 1+x2 +с x cot-1x +In/ 1+x² + C None

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Which of the following gives /₁ O 5tanh-¹ (5x) + C Otanh-¹ (5x) + C Ocoth ¹(5x) + C 5coth-¹(5x) + C…

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Q: 1/6 aresin(3) dx =

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Q: Y₁' = 3Y₁ + 1/₂ ل3 Y/₂ = 2y + 2y₂

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Q: Determine and y such that 0 [xy 139+223-412,3] = 2x y -5

A: To determine the values of x and y.

Q: b) (9x²-6x+26) *

A:

Q: Evaluate V3x? +5 dx xV3x* +5 , 5V3 in/J3x + 3x² +5)+ C xV3x² +5_ 5/3 In 3x + V3x +5)+C A. C. 2 2 6.…

A: Use the method of integration by parts by assuming '1' as the second function.

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: 9. Simplify sec² x - 1 sec² x

A: secx=1cosxI=sec2x-1sec2xsin2x+cos2x=1

Q: |(5z* + 3z*) (4x³ + 3x*)° dæ

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Q: Verify that (cotx-cscx) (cotx+cscx) + 1 = 0.

A: (cotx-cscx)(cotx+cscx) + 1 = 0.

Q: A tank initially has 100 gallons of brine containing 5 lbs of salt. The mixture is kept well-mixed.…

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Q: Integrate: / 7++96 dæ 2+x+96, +16x

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Q: Find X bi -

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Q: P0HXでにん スXt1ocx

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Q: nd the ndcaed liml lim 15X +3

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Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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