By using the substitution u = 4x + 1, evaluate (4x+1) dx 1 x²+x+k 4 4x2 + x + k 1 x' + x + k (4x + 1) + k

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

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Q: 3. (a) Determine S 2xe3*dx by using integration by parts.

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Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: 1. Evalute the improper integral 3x dx. 1+ x2 -1

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Q: Evaluate the integral dx 2xx - 3x? A -In 4 V2x + V3 +C 1 V3+ 2x B In +C 2/3 V3-2 +C In 2/3 "/7x + /3…

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Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

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Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: 1 V5x + 4

A: We have  ∫1x dx=2x.

Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

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Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Evaluate the double integral 1 2x+1 LL.** Select one: | None of them 113 x² dy dx

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Q: 3 Evaluate the integral: dx 2 Vx -1

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Q: 3,2 Evaluate the integral xx + x +2 dx%3D

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Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: Step by step

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

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Q: find the integral of (4x − 6)5 dx; u = 4x − 6

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Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: To evaluate / (3x2+ 1) In x dx using integration by parts, it is best to let A u= 3x2; dv= In x dx…

A: Integration:- A integral assigns numbers to functions in a way that describes displacement, area,…

Q: Evaluate the integral. V36 – x² dx = 18sin- +xV36 – x² + c V36 – x² dx = 36sin--xV36 – x² + C / V36…

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Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" - Зу" + Зу'…

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Q: Step by step

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Q: 4. Evaluate the integral 3x2 + 13.x + 11 dx I (x+1)(x +2)²

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Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: Evaluate the integral Зx2 — 4х — 9 A В + C dx using x3 – 2x2 – 9x + 18 - 2 x +3 – 3* х — х — 3x2 –…

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Q: 2. Evaluate the integral x(3 – 5x) (3x – 1)(x – 1)2 dx

A: To solve the following integral

Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

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Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: 54x + 21 Evaluate dx where 9x2 + 7x + 8 > 0. | 9x² + 7x + 8 First substitute u = 54x + 21 -dx 7x + 8…

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Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: Find the integration inner product on C[-3,3] of the given functions. f(x) = 16x g(x) = 3x² (f, g)…

A: Explanation of the answer is as follows

Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

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Q: Use multiple application of the trapezoidal rule to numerically integrate : f(x) = = 400 x ² - 900…

A: It is a Numerical Analysis problem. Let us estimate the value of the integral numerically using…

Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C…

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: