Guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative.) 6 dx 6 dx 0 (Type an exact answer in terms of e.)

Q: Evaluate the definite integral from e^49 to e^81 ([e^49,e^81]) of the equation dx/xsquareroot of lnx

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Q: 2. dx find this integral by using Simpson's rule e

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

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Q: Find an antiderivative of the following function by trial and error. Check your answer by…

A: we need to use trial and error method

Q: (c) (1) Show that e +2)e +c, where c is a constant of integration. 5 "dx

A: We have to find the integration of the equation  ∫e(i-2)xdx

Q: Find the exact value of the definite integral below, using the substitution u = x - 1²/1. X (√6+√2)…

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Q: Question 010: Complete the following question involving basic integration techniques. Given the…

A: Below is the solution to the question.

Q: e Inx dx 1

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Q: Differentiate  G(t)= Sinh(In t) G'(t)=?

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

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

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Q: 1 dx 1) Evaluate the integral sinh r

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Q: If U, is a function whose fifth differences are constant and U, dx can be expressed in the fom pU…

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

A: We have to find value of given integral.

Q: 2. Given x³+ y3 = 6xy dy? a. Use Implicit differentiation to find ? dx b. Find the equation of the…

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Q: 1. Evaluate the indefinite integral and check your answer by differentiation 6dx a) S (z – /2) b) J…

A: To evaluate the indefinite integral. a)  ∫6 dxx - 23 b) ∫cos2x2 dx

Q: Find an antiderivative of the following function by trial and error. Check your answer by…

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Q: Given ſ 97**sin x (1+ 2 cos x) dx. There is an appropriate value of u so that the resulting integral…

A: given ∫912x+sinx1+2cosxdx this can be written as ∫3212x+sinx1+2cosxdx⇒∫3x+2sinx1+2cosxdx put…

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

A: Let's find.

Q: Evaluate the definite integral (За3 — 5а + 2) da fo 5а + 2) dx — a) Find an anti-derivative +C b)…

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Q: II. Find the value of the definite integral xV[a2 – 9| +7 dx 0.

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Q: (a) Integrate the following function; i) SG) dx 1+9x² ii) S dx (b) Differentiate y = cosh-1(x² + 1)…

A: 5(a) (i) Given integral is ∫91+9x2dx ∫91+9x2dx=9∫1919+x2dx=∫119+x2dx=∫1132+x2dx Hence,…

Q: Evaluate the following indefinite integral. dx dx = (Type an exact answer.)

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Q: By making the change of variables t = x? in the integral that defines the gamma function, show that…

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Q: Find the following definite integral where A is a constant and A > 2: | (10z + 17z +1) dx = %3D

A: We have to find the integral of∫2A(10x3+17x+1)dx, where A>2. Applying the sum rule of…

Q: Evaluate the definite integral. 1/2 + a? dx (a > 0)

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Q: dx: Consider the indefinite integral e* +4

A: We have to evaluate the integration by substitution.

Q: dy using the method of logarithmic dx 4 tan a Find Let y = (In x)“ differentiation. Express your…

A: We can solve the given problem using concept of differentiate above equation with respect to x

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt cos?(t) V7 + tan(t)…

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Q: 3x – 4 What is the value of the definite integral dx? Enter your answer as an exact fraction if…

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Q: . Given 1 [(5x+ + = + 1) dx a. ) Evaluate the indefinite integral above b. Evaluate the integral…

A: The given integral is ∫5x4+1x+1x2dx

Q: Find dy by implicit differentiation, given that eT° Y + 7 ln (x) = y. Your answer could involve both…

A: To determine the implicit derivative of the function.

Q: Can i get help step by step?

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Q: Q4: Find the integration for the following functions: - (answer three only) sin(lnx) dx 3-…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: 1. Given a. b. C. ixª + 1 1 + dx ) Evaluate the indefinite integral above Evaluate the integral…

A: Note: According to the guidelines of Bartleby we will answer only first question for you. Kindly…

Q: Every answer I get is wrong please explain the steps to me.

A: We are given indefinite integral.

Q: A. Find dy/dx of the following. 4. y In(ln x") 5. y = cosh(In x) – sinh(In x) 6. y = log In x

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Q: Evaluate the definite integral. 8. dx 3

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Q: Use a change of variables or the table to evaluate the following definite integral. 10 e 2X dx 2x…

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Q: Find the following integral. Note that you can check your answer by differentiation. / (t+ 1)? t2 dt…

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Q: For the function below, write the differential. f(x) = In(1 + x?) %3D ] áe dy = dx Calculate dy for…

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Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

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Q: dx 8. Find the definite integral Ans:

A: Given integral  I=∫56x2-25x2dx

Q: Find the first derivative or h'(s) of the function below using the techniques of integration: 4 h…

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Q: aluate the definite integral. x6 + a2 dx (a > 0)

A: We have to find the integral

Q: Q;: Find the integration for the following functions: - (answer three only) In(x²+x)-Inx-e!nx 3-S-…

A: Given  1) The integration is  -∫π01-cos(2x)2dx .

Q: Which of the following is the best integration technique to use for x e* dx? a. The integration by…

A: When two different functions are given, in which one function seems to be diminished by…

Q: Find an antiderivative of the following function by trial and error. Check your answer by…

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Q: Calculate SN given by Simpson's Rule for the value of N = 6. I cos(2x² ) dx (Round your answer to…

A: given the expression is , SN given by simpson's rule for the value of N=6 ∫01cos(2x2)dx