Use the Log Rule to find the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) x3 dx

Q: The value of the following integral is log. dx e-1 O 3/2 O 5 O 5/2 3

A: We have to evaluate the integral ∫e−1e2logexxdx. Substitute logex=u ⇒1xdx=du And limit of u is u=-1…

Q: dx I = a² +x²

A: Given query is to find integration of the expression.

Q: Which of the following indefinite integrals will result to logarithmic expression? O Stan(sinx)cosx…

A: topic - integration

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 the following integral is |log,r| dx O 5/2 O 3 O 3/2 O 5

A: Here option c)  3/2 is correct. Here we solve this integration using substitution method.

Q: 3 2 4x 6. S x´e* dx

A: ∫ eau du = 1a eau +C ; where , 'C' is an integration constant .

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

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Q: Use the Log Rule to find the indefinite integral. (Use C for the constant of integration. Remember…

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Q: +. dx (assume x > 0) 5) S dx 3x+12

A: Here we solve indefinite integral.

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

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Q: Evaluate the following indefinite and definite integrals: S(x' +e* )dx

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Q: dx

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Q: Evaluate the definite integral on the interval [e, e^64] dx / x sqrt{ln(x)

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Q: Evaluate the following integral. 10 0 4 log 11 (x + 1) X+1 -dx

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Q: Which of the following indefinite integrals will result to logarithmic expression? 2 A dx (2x+7)2 B…

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Q: Solve the new Integral using the General Log Rule. Then, back-substitute x into the equation.…

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx

A: see below the answer and calculation with steps

Q: dx I = е. a² +x²

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Q: Use the Log Rule to find the indefinite integral. (Use C for the constant of integration.) dx

A: Let z=x2+2dz=2xdxxdx=dz2

Q: Evaluate the following definite integrals log(1+ cosx) dx.

A: Introduction::

Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

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

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Q: Recall that the constant term, C, cancels out when evaluating a definite integral and therefore, the…

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Q: Sx sech ? x dx

A: To evaluate the integral: ∫x sech2x dx Solution: Integral by parts states that: ∫u dv=uv-∫v du…

Q: Vex – 1 dx c2

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Q: | (e" – 2)2 dx

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Q: Which of the following integrals will NOT result into a natural logarithmic function? 5x xp: sec x2…

A: Evaluate each integral separately.

Q: dx c1 16. 21 1)

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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: +/t%edt 1. 2. Se-x/2dx 3. 3*e*dx

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Q: /2+In x dx

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Q: Use this figure to find the following definite integrals:

A: The figure given in the problem represents the graph of the function y=f(x). The region under the…

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

A: SOLUTION-

Q: Evaluate the following definite integrals log(1+cosx) dx .

A: Given the definite integral

Q: 7/4 A (sint + cost)dt

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Q: n4 dx b. 2 х-3

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Q: Evaluate the definite integral. e4 – x dx 14

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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: Evaluate each of the following indefinite integrals using substitution, expressing your final answer…

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Q: logz x (Hint: rewrite using change of base first) a) S" dx

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Q: (log r) d.x 1+x²

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

Q: Evaluate the definite integral. 1 e dx

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Q: Which of the following indefinite integrals will result to logarithmic expression? 2 (2x +7)2 B None…

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Q: L(3x+e")dx Jo

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx

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Q: Consider the definite integral 10 300x dx 1+ e*

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Q: Evaluate the following integral or state that it diverges. 00 4 2 sec dx

A: Given

Q: Evaluate the definite integral. e 1/x dx

A: Now consider,

Q: Evaluate the definite integral. e + 6 dz e? + 6z

A: We need to evaluate the following limit ∫01ez+6ez+6zdz                             .........1

Q: (x²–x) 1.) S-x) _dx x3+15+12

A: Note: As per company policy we are supposed to solve only 1 question, SO, kindl