5х — 2 dx x² +1 - 10.)

Q: Find the following integral: S- -4 /x² dx x3

A: Explained below

Q: Evaluate the following integral: 1 dx, (x² + 6x)/2 x > 0.

A: Indefinite Integration

Q: 1. S(In x)² dx

A:

Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

A:

Q: Evaluate the following integrals. 1. S sin*(2x) dx

A: As per bartleby guidelines we only give first question answers.

Q: Evaluate the following integrals using techniques studied x(x+ 5)* dx 2. 4x cos (x² + 1)dx

A: Given: 1. ∫xx+54dx2. ∫4xcosx2+1dx

Q: e2x sin(e)dx cos (ezx)+3

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q1. Evaluate the following Integrals 1 dx xVx

A:

Q: Evaluate the following integrals: 2. Inx de sin 3x 3. dx 1-cos 3x 4. S 32* dx 5. S(e* + 1)°e*dx 6.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Evaluate the following Integrals. dx V1 – 4.x2 4. -

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Q: Evaluate the following integrals a) dx J (2x - 1)3 6x dx b) 2.

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Q: Determine the following integrals: ³ In r dx and

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Q: 6.) | dx 4 – x²

A: Let the given integral is ∫x34-x2dx

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx -TT/3 7. p² sin 0 de dp Jπ/6 S3

A: The integration of the integral is  6) 3x2y2 7) (row) 2sin(theta).

Q: Evaluate the following integrals 1 3x 2x + y²)dydx a.

A: Solve the following

Q: Evaluate the following integrals: (a) dx x²/x² – 16 - (b) sin x cos xdx (c) x – 3 x² + 6x + 5 -

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Q: 12.) / 5a2 – 14x + 6 dx 23 – 3r2

A:

Q: Evaluate the following integrals S²z sin³ x cos20 x dx 2

A: We have to evaluate the integral ∫-π2π2sin3x cos20x dx.

Q: 2 - dx x2 +1 01

A:

Q: In x dx 7.) /

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Q: Evaluate the following improper integrals provided they conver dx a) S Vx-x2

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Q: Evaluate the following integrals.

A: To integrate: ∫0π2e-3xcosxdx Use integration by parts:      ∫u dv = u v - ∫v du Let   u =cos(x)…

Q: Use the substitution technique to determine the following integrals:

A:

Q: 5.) / a In a dx

A: Given, ∫x3lnxdx  Using Integration By Parts, ∫u dv=uv-∫v du Here u=ln(x), dv=x3…

Q: Evaluate the following integrals. 1. sec-a dæ cos Va dx Væ csc /æ 2. x2 dx - 3.

A: Integration by parts

Q: Evaluate the following integrals.

A: Given that: The integral is ∫exe2x + 2 ex + 17 dx .

Q: Either evaluate the following improper integrals or show that it diverges. +oo 1 (i) - dx +oo (ii) 2…

A: We have to evaluate the given integrals.

Q: Evaluate the following integrals dx S; x+V4x2+1

A: Given : Integral ∫dxx44x2 + 1   To find : Evaluate the given integral ?

Q: 1 8.) / dx (x2 + 16)3/2

A: We have to evaluate the integral: I=∫1x2+1632dx In this case we do use substitution method, so let…

Q: Evaluate the following improper integrals or show that they diverge. c+00 dx (a) x5/2 1 dx 1+ x2 (b)

A: Let's find.

Q: 2. x² V1-x? dx_

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Q: 6 sec*x dx

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Q: Evaluate the following integrals. Reasonable work is expected! 1.) 4x²e" dx

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Q: 4 x*dx X-1

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the following integrals. Show all the necessary solutions. ² dx 1.

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Q: Which of the following integrals does not require substitution? o fxsin(1 – x²)dx dx 5x²/2 + x3 •…

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Q: Evaluate the following integral. dx 1+ e2x - In 13 ex dx = 2x 1+ - In 13 (Type an exact answer.)

A: ..............(1) take ................put it back in equation 1

Q: Compute the definite integral below using the results in S '5 I x² dx

A:

Q: Evaluate the following integrals ii. fx cot-'x dx .

A: Solution is given below:

Q: Evaluate the following Integrals 1. f 5 dx 2 ledr

A: We have to find the integral

Q: Evaluate the following integrals. SHOW C 1. e2*-1)² dx e2x

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Q: 1) Calculate the following integrals. b) √₁6x²=1 -dx

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Q: Evaluate the following integrals: 2r3 2) 2x2 + 1 - dx x² - x 1) | dx

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Q: / FVA 12.) dx x²/25 – a²

A: Given integral is ∫1x225-x2dx Substitute x=5costdx=-5sintdt

Q: 1 dx x2 (1) x=1 x=1 (2) et dx x=-0 x=-∞

A: (1) Consider

Q: Evaluate the following integrals: а- T/2 2cosx dx 1+ (sinx)² -T/2

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Q: [5]. Calculate the exact values of the following definite integrals. Srsin(2.x) dr (a) o dx x² - 4…

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Q: 2. dx

A: Given: ∫ x3ex4-3dx

Q: 1 1 1 dx x+2, x+1

A: We can solve this as follows: