Evaluate the integral Select the correct answer. ( x + 6 In ( e* - 1 ) + C ○ 4x-31n (e*-1) + C 6x +41n | ex-1| + c - 4 In | ex-1| + C Ox-4 1+ 3e 1-e* dx

Q: Evaluate L-1{ -(-e¯™s+4T8+ 2+1

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A: Explanation of the solution is given below...

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A: Solve the problem using partial fractions

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

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Q: (x+2)2 dx (x+2)3 +C (A + 2x+4 In x +C +4x +4 In x + C (x+2)3 D -In x +C 3. B.

A:

Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

A:

Q: x³ + 27 dx . x+3 Evaluate x3 +9x + C 3 x3 3 +žx²+9x+C 3 x3 + x² – 9x + C 3 2 x3 3 x² + 9x+C 2 3

A: We know that, The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

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Q: + 9x + 27 dx (x + 3) (x² + 9)

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Q: Verify that x² +1 = (x² + v2x + 1)(x² – V2x + 1). %3D

A: **Since you have asked to solve question no. 42, you will solve that question.Question 42.We need to…

Q: x-1) 1/6(x+2) 16/3- (x+1) 1/2 x-1) 1/6(x+2) 16/3 (x+1) 1/2 x-1) 1/6(x+2) 16/3 + +

A:

Q: 1 e2x + 5ех 4 e2x + 4ex

A: Given: ∫ 14e2x+5exe2x+4ex dx= 14∫ ex+20ex+4 dx    (Multiply and divided by e-x)

Q: Integrate the given expression. |(4x? – 7x) dx A 7 2+C X 2 3. 7 X + C 2 В C none of these D x 3 + C…

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Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: 3x + 3x3 – 5x2 + x -1 dx x2 + x-2 Q4, Evaluate

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Q: Evaluate using the substitution method. √ dz 2x4 (6 +x5) 4 2 1 [(26²du) - 15 (6+23)² + = = + C +x5)³…

A: Given ∫2x46+x54dx

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A: Using bodmas  First bracket then division then multiplication

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Q: B Sin3X 6653X + X3

A:

Q: 2x+ス+ dx ャX-ス

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: d 4х +11 15. In((x + 1)(2x + 9)) dx (x + 1)(2x + 9)

A: Given:ddxlnx+12x+9

Q: Evaluate: (x+1)x* +4)* dx x +1 x² +4 + 4

A: This question is taken from Indefinite integral in which we have to find the integral value of the…

Q: Find 2 2 [²³²³ (5x + 2y) dxdy

A:

Q: A - 3 In 1x³ 3x²1+C BIn 1x³ 3x²1+ C x²–2x x3 3x² C dx In 1x³ 3x²1+C In 1x³ 3x²1+ C -

A: The given integral,    ∫x2-2xx3-3x2dx