Assume that A, B, and C are positive coefficients. Symbolab.com solves this integral using integration by parts: salmia (+) a dx. (Bx+C)3 Solve the integral by a simpler method.

Q: Evaluate the integral | a (2° – 5)26 dx, by making the substitution u = x6 - 5. +C Note: Your answer…

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Q: 3tan a sec? x dx (4+3tan=)* 2

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Q: Evaluate the integral. -1 sin (9x) da = V1-81x 6. +C

A: We will solve the following

Q: (In 1ºx+ 4lnx) *dx

A: Given: - The integral is, ∫(ln10x+4ln(x))8dxx To find: - The solution of the given integral. include…

Q: e2 sec(e2")dr

A: We have to solve the integral: ∫e2x sece2xdx In this case we will use substitution method. So…

Q: f1+z+² /1+z+z? + 3z*dz

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: sec²(/T+1) dr. 9.

A: To integrate ∫sec2x+1xdx Substitute u=x+1 Then         dudx=ddxx+1       =ddxx+ddx1       =12x12-1+0…

Q: Evaluate the integral 18 - 6)"da, by making the appropriate substitution: u = *(=* - 6)*dx = 18…

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Q: The integral 9x? – x3 – 18x dx MUST be -1 evaluated by breaking it up into a sum of three integrals:

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Q: Evaluate the integral |(2x + 6) (2² + 6x + 6)°dx by making the substitution u = x² + 6x + 6. + C…

A: Indefinite Integration

Q: x² + 2 xp (х — 2)(x2 — 2х + 2)

A: The given integral is: I=∫x2+2x-2x2-2x+2dx   We know that; ∫1ax+bdx=1alnax+b+C

Q: Solve the integral- (a) d x (b) Syos sinx an

A: We have to solve the following integral -  (a) ∫x9-x2dx

Q: Evaluate the integral (* - 11)"dz, by making the substitution u = x* – 11. + C

A: We will solve this integration by substitution

Q: For the integral e4z – 10 dæ, if we use the substitution u = 4x – 10, what will be the new integral?…

A: We use substitution method

Q: Complete the square and find the indefinite integral. x2 dx V 2x - x

A: Given∫x22x-x2dx∫x22x-x2+1-1dx∫x21-(x2-2x+1)dx∫x21-(x-1)2dx

Q: state what method applies and how one applies it, but do not evaluate the integral:

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Q: Define a substitution variable u and write ;dr in terms of only u. (2x – 1)2 You do not need to…

A: Given: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Use either integration by substitution x² +1 S x³+3x+5 dr given that A-5 and B=7 Give your answer to…

A: We need to evaluate the following integral ∫ABx2+1x3+3x+5dx, A = 5 and B = 7

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

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Q: 1 dz I|z||=2 2z – 3

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Q: 3x²-2 do 3 2x - 4x

A: Here we will solve the given integral,

Q: B. Solve for the integrals of the following: 3x2 dx -5 COS xesinx -dr c) ] 4 4x a) b) dx esin z

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Q: Choose the most appropriate answer The integral : S(6x + 7e*)dr = %3D

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Q: dx c1 16. 21 1)

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Q: e4z dz I|z-1||=2 z – 4

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Q: a) S In Gxt1) dx 2.

A: In this question we have to find the Integration. Formula Used, - Chain Rule. - ∫lnx=1x+C

Q: Evaluate the integral 3 I| 81x*/y² + 16dydx 3x by reversing the order of integration.

A: To find:- By reversing the order evaluate the given double integration

Q: Evaluate the integral using the following values. Ca*dx = 1020, Sz dz dx = 30, C da = 6 %3D Solve :…

A: Given integral, ∫286x3-12x+5 dx

Q: use the indicated substitution to evaluate the integral.

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Q: dx 2x² 2. + 6

A: Given ∫4x2x2+6dx In order to solve the given integration first substitute 2x2+6=u and then proceed.…

Q: Give the appropriate trig sub that would be used to evaluate dx. Do NOT Vx² – 16 solve the integral.

A: Given:     ∫x3x2-16dx

Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: Write the iterated integral ∫10-10∫200 (x2y + 2xy3) dy dxwith the order of integration reversed.

A: To evaluate: ∫-1010∫020x2y+2xy3dydx. Evaluating the integral.…

Q: Find the integral 52? + 3х — 2 dx +C x3 + 2x?

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Q: Write the integral in terms of u and du. Then evaluate. xV9x + 4 dx, u = 9x +4 (Use symbolic…

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Q: Evaluate the integral. 4 – e2× dx = +C

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Q: Let a, b, and C be a constant, verify the following indefinite integral. IVa+bx dx 2 (3bx – 2a)(a +…

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Q: Determine the integral solutions  fro which x and y are positive 2x + 5y = 17

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Q: Which of the following integration expression can be transformed into integral of power (Ju"du). 2…

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Q: EC) Determine the value of the definite integral -1 ² (4x³ + 5)³dx .

A: The given definite integral,     ∫-10x24x3+53dx

Q: Find the indefinite integral. 7x + 4e5x dæ ebx + 2e6x Integral = + C

A: Solve the integration .

Q: Sx²e=* dx Sx²e¬

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Q: *) dx x° tan(x .3 프4

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Q: 4. 1) ŝ dy

A: The given integral is, ∫y7y4-113dy The objective is to solve the integral by substitution method.

Q: Evaluate the integral (2x + 4) (2² + 4x + 2) dz by making the substitution = x² + 4x + 2. Submit…

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Q: Use the substitution formula to evaluate the integral. T/20 (1.clan 5x) sec2 5x dx Select one: O A -…

A: Substitute the trigonometric function in some other variables.

Q: 2x2 + 2x + 11 dx (2x + 3)(x² + 4) (c)

A: Evaluating the integral using partial fractions.

Q: Evaluate the integral + 3)(x² + 3x + 5)* dx by making the substitution u = x² + 3x + 5. + C NOTE:…

A: We can evaluate the given integral by using the substitution u=x2+3x+5 and applying the following…

Q: Evaluate the integral *(2 – 6)"dz 10 - by making the substitution u = x° - 6. + C NOTE: Your answer…

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Q: Find the definite integral c2 2127 dx z13z2 1

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.