Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.) - 3) dx - 4x

Q: Given the integral ( 12x3 + 7 dx -5 Use the integral table to help you find the Anti Derivative of…

A: To evaluate: ∫-5712x3+7 dx We know that  ∫xndx=xn+1n+1, ∫kf(x)dx=k∫f(x)dx and  ∫abf(x)dx=F(b)-F(a),…

Q: Use the Change of Variables Formula to evaluate the definite integral.

A: Use the Change of Variables Formula to evaluate the definite integral.

Q: II. Perform the integration. sinh?(e-") 4. e# cosh(e-¤) dx

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Q: In solving for the -dx, what technique is suited to solve for its integral? x²+1 A integration by…

A: Let I = ∫ x3 + 1x2 + 1dx = ∫x3 ( x2 + 1)dx + ∫ 1x2 + 1 dx, As we know ∫ 1( x2 + 1) dx = tan-1 (x) ⇒I…

Q: Find the definite integral: (x² + 2x)dx

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Q: Find the value of the following definite integrals. Show your solution. L₂(x¹+4) dx 2. (cos x + tan…

A: Topic = Integration

Q: dy =

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Q: b) (x-1)3 1 dx = ?

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Q: (- + =) dx when evaluated is equal to 3Vx, 11 Find the value of a. The definite integral 12

A: Given problem:- Th value is given as  ∫49-xa+13xdx=-1112 The integration formula is expressed as…

Q: II. Perform the integration. sinh? (e¬) dx eª cosh(e-¤) 2 4.

A: We have to find value of given integral.

Q: Solve the ODE by integration or by remembering a differentiation formula. 1. y+2 sin 2mx = 0 2. y+…

A: According to our company's guidelines I can only answer first three subparts of the questions since…

Q: Evaluate the definite integral. (Assume a > 0.) 'a²/5 x*Va? - x5 dx

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Q: II. Perform the integration. 2x + 1 2. dx J 2? + 8x + 25

A: Explanation of the answer is as follows

Q: b) By using appropriate substitution, solve the integral 7x dx. (1–4x)"

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Q: Зу? + у — 1 y?

A: We have to solve the given definite integral: ∫123y2+y-1y2dy Rewriting the integral and solving the…

Q: Find the definite integral.

A: The given integrand is, fx=-sinx. The limit of the integration is, -π to 2π3. The objective is to…

Q: (36 – x² \dx Evaluate the definite integral:.

A:

Q: Determine the indefinite integral | 5x4(x5-6)8 dx by substitution. (It is recommended that you check…

A: Let's find.

Q: dx (4x²+5)' Evaluate the indefinite integral |

A: We will solve the integration.

Q: -2 What is the value of the definite integral e* dx? -4

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Q: |(x? - 1) dx. Use the definition of the definite integral to evaluate

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Q: ne J反Inx dx

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Q: II. Perform the integration. sinh?(e¬") dx e# cosh(e-¤) 2 4.

A: Put e-x=t then solve it.

Q: csc? (2x) dx 1 + 5cot² (2x)

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Q: x² To solve the indefinite integral dx, rewrite the (1 + x²)2

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Q: T/6 sec² xdx 1+9 tan? x

A: Given query is to find the value of the integral.

Q: Evaluate the definite integral?

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Q: 4. Sx3 In x* dx

A: Integration by parts: - Integration by parts is a technique for combining the output of two or more…

Q: refer to f -3)dx x-2 What will be the answer when the integral is evaluated? Show your solution…

A: Integration of the given integrand x2-3x-2 can be found with the help of the division algorithm and…

Q: Evaluate the definite integrals a) (бх? — - 2x – 10) dx = / (x+ 4)² dx = b) 1 c) (x* – x³ ) dx - ||

A: Some of the properties of integration  ∫abf(x)dx=F(b)-F(a) ∫xndx=xn+1n+1+C…

Q: Zvaluate the given indefinite integral. Show your detailed solution. (Non-anonymous questionO) 2x2…

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Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: Find the indefinite integral and check the results by differentiation? (4x^2 + 3)^2

A: I=∫(4x2+3)2dx =∫(16x4+24x2+9)dxintegrateI=165x5+8x3+9x+c    where c is any constant

Q: e4x dx 6+ e4x

A: Given: I=∫e4x6+e4xdx

Q: Decide whether you can find each integral using the formulas and techniques you have studied so far.…

A: Given: I=∫2dxx2+4 we know that ∫dxx2+a2=logx+x2+a2+c                                      ..1

Q: | sec* x tan x dx

A: Given integral is ∫π4π2sec4x tanx dx

Q: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: За? +8х —12 dx x3+7x²+12x 3x +8x- -12х

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Q: dx 8. Find the definite integral Ans:

A: Given integral  I=∫56x2-25x2dx

Q: Find the indefinite integral by using the substitution x = 6 tan(e). (Use C for the constant of…

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Q: J-4) dx. Use the definition of the definite integral to evaluate

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin 2x 48 + cos? x xp

A: The given integral is- I=∫sin2x48+cos2xdx Let 48+cos2x=t Differentiating above equation w.r.t x-…

Q: Solve the integral shown below. Show your solutions. 3xe ²x dx

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Q: Find the definite integral 10 (2х — 3) dx

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Q: State the trigonometric substitution you would use to find the indefinite integral. Do not…

A: Here, to evaluate the given integral use the trigonometric substitution. ∫x2(x2-36)32dx

Q: +1 dx x+1 10.

A: As we know that the power rule: ∫xndx=xn+1n+1+C ; n≠-1 From the given problem: I=∫01x3+1x+1dx

Q: f(x) = e-* cos(2x) dx

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Q: Use familiar area formulas to evaluate the definite integral.

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Q: 5. (1+6x) (6)dx

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…