Use the Exponential Rule to find the indefinite integral. (Use C for the constant of integration.) 7xe Sx2 dx

Q: X cosh? dx 2 -In2

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Q: Evaluate each indefinite integral by finding the antiderivative.

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Q: Q17: Find the indefinite integral: Sezt (e2x + 1)° dx

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Q: Write an equation given the following: m = 3, y-int = -1

A: The General equation for straight line is Y = mX+C. Where m = slope of straight line. C =…

Q: Determine how large the number a has to be so that dx

A: To solve this problem we will first solve the integration and then use the concept of linear…

Q: e dx -5

A: Width of the interval [-5,5]= 5-(-5)=5+5=10n=number of subintervals. Width of each…

Q: [eln ax - 2x log(x² + a)]dx 3.

A: Given: ∫eln ax-2xlogx2+adx To Find: Value of the given integration

Q: The value of L(e2t sinh(2t)) =

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Q: Solve the following integral step by step senx -dx ex

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Q: 1/6 dx 3.S T1-9x2

A: Solve the definite intregal

Q: In the given equation as follows , complete the square and find the indefinite integral? See the…

A: Assume or convert x in some from to make the equation more easy to solve. Then perform integration…

Q: Evaluate the following indefinite integral. Use C for any constant of integration. 56 dx x2 – 49

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Q: (b) Solve the following integrals by using substitution and exponential rule and verify the answers.…

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Q: х2—4х+6 dx х-1

A: We have the given integral as I=∫x2-4x+6x+1dx Let us consider that, x+1=u⇒x=u-1dx=du Therefore,…

Q: ate the integral. (If the quantit 8. dx (x2 + 4)2

A: The given integral,                ∫-∞∞xx2+42dx

Q: Given ∫(−6x5 +5x3 +1)dx, evaluate the indefinite integral. Do not include +C in your answer.

A: To calculate the indefinite integral of the expression -6x5+5x3+1. To integrate the provided…

Q: Зу? + у — 1 y?

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

Q: I Evaluate the following expressions by basic integration: dx 2. ,(x + 3)(x – 4)dx

A: Given

Q: 8) S xe5x dx

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Q: Perform the following integrations: 9. 10. dx

A: To evaluate the given integral.

Q: 1. dx x-19-x

A: Given :∫dxx49-x2

Q: Evaluate the definite integral: - 6 e!/I dx

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Q: Express the integral in terms of the variable u, but do not evaluate it e8r-7 dx; и — 8х -7 NOTE:…

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Q: evaluate using Integration by Parts, substitution, or both if necessary.

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Q: ne J反Inx dx

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Q: Perform the indicated multiplication and then integrate. Use Cfor the constant of integration.…

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Q: csc? (2x) dx 1 + 5cot² (2x)

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Q: Evaluate the integral dx by making the substitution u = 5x2. After substituting we have: (in terms…

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Q: Solve the integral. Show your solutions. Sỉ XUÂN ĐÃ

A: The given integral is ∫13xe3xdx. Solve the given integral.

Q: S x³ e ³x dx

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Q: 7) Se3 V1+ e3xdx

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Q: Use the Change of Variables Formula to evaluate the definite integral. dx (x2 +2)° (Use symbolic…

A: Answer and explanation is given below The formula of integration is ∫xndx=xn+1n+1+c Let…

Q: dx 2x x2

A: Let I=∫1-12xdxx2

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A: (a) To integrate: ∫ex2dx We know that, ex=1+x+x22!+x33!+⋯⋯=1+x+x22+x36+⋯⋯ Now, ex2=1+x2+x42+x66+………

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: Determine how large the number a has to be so that dx

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Q: (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that…

A: The solution is given as

Q: Find the indefinite integral

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Q: 00 e-st cosh t dt

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Q: (log r) d.x 1+x²

A: The given integral is, ∫0∞logx41+x2dx

Q: Integrate (2x + 1)" dx with respect to x.

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Q: . Determine how large the number a has to be so that dx

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Q: Evaluate the integral xe5x? dx by making the substitution u = 5x2. After substituting we have: (in…

A: Use substitutions to integration

Q: Using integration by parts, solve the following indefinite integral |x?eš*dx

A: We will evaluate the given integral.

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: Q1: what is on (3x) SI2 dx x2

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Q: T/2 sin & cas Ode sinte

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Q: Evaluate the integral, if possible. (Hint: use the table of integrals and substitution)

A: Use the properties of indefinite integral to simplify.Let w = x^4.Calculate dw and simplify using…