1- (In x)? If u= In x, then dx=?

Q: xe 2, x Cosz dx

A: Integration by parts, ∫udv=uv-∫vdu u is the first function Given integral, ∫x exdx

Q: 5. Integrate: [tan(7x)dx

A: 5) The given integral is ∫tan7xdx

Q: |2tan x In (cos x) dx=

A:

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: Find

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Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

A:

Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: 22. Evaluate So Si S dx dy dz.

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Q: 9. Vy + dy 415

A: We will be using the given rules to evaluate the answer

Q: -1 Integrate Jxsin 'dx

A: To evaluate : ∫01x sin-1x dx

Q: 2 dx =

A:

Q: In(x) dx; u = In(x), dv = x³ dx

A: Use integration by parts method.

Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: r(10,3,3) dx (1,1,1) dy dz. - -

A:

Q: Evaluate f, f,(1-2) L(-dy dx dz

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Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

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Q: S sin Vat dt

A: Let the given integral be: I=∫sinat dt

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: 1. dx Evaluate 0, et +e-*

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Q: d - In(u²) dt dx et

A:

Q: Prove d [sin-! lu(x))]= I dx dulx) %3D NI- Culx)]? dx

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Q: d tanh (u) du Sech (u) dx dx

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: If y- sinhx then prove that dy dx

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Q: 3 sinº x dx 4 Show that

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Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

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Q: 1. Use Fermat's principle to find the path followed by a light ray if the index of refraction is…

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Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

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Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: Evaluate L S dx dy. O 1 2/3 1/2 O 2

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Q: In (5x) dx 1 In (5x) dx = (Do not round until the final answer. Then ro

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Q: Evaluate dz dx dy. Ji

A: Do not change the order of integration. Perform the integration in the same order as given and take…

Q: cosh(In x) dx

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Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: 1 B3. Evaluate dx, using substitution method.

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Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

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Q: Integrate: Sx e* dx.

A: