Rewrite the integration in terms of u. 2x dx = du x² + 16

Q: Evaluate the integral: fe2 /1+ e2 dx

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Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: Solve the two items using Integration by parts. 1. (x' V9-x? dx

A: Question - 1:- Given: ∫x39-x2dx Formulas used: ddxxn=nxn-1ddxconstant=0ddxfgx=f'gx·g'x        Chain…

Q: Reverse the order of integration in S S(2xy + 1)dxdy and then evaluate.

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Q: (10xy + 8y - 32y +7)dx+ 2(x +2xy– 4x)dy =

A: To solve the differential equation , I have used the method of exact differential equation and then…

Q: use the indicated substitution to evaluate the integral.

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Q: Solve the integral. dx 9. J Ta – x)(b – x)

A: The given integral is, ∫dxa-xb-x To solve the given integral, we use the partial fraction,…

Q: Q3/ Evaluate the integrations: Seax cos (e*) dx. A)

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Q: Find the integration to de 0. a+bcos² 0

A: Given ∫02πdθa+bcos2θ. The given integrand is even function  We need to evaluate the above integral.…

Q: Evaluate (3 t + 5) cos () d+ using integration by parts .

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Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: Evaluate the integral -7 dx Væ +1+ Vx + C

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Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: Evaluate the integral. V4– e2¤ dx +C

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: * = cos(x + y), when x = 0,y = %3D dx

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Q: Integrate the following using the basic rules of integration and substitution 1. fx2 +5x3-x-³ dx

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

Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

Q: Use either integration by substitution or integration by parts as needed to evaluate S³= A B x²+1…

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Q: 1) I = S(x² + 2x) cos x dx %3D

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Q: Solve the general solution using the integrating factors by inspection (x³y³+1)dx+x⁴y²dy=0

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Q: Q1/ Evaluate the integral: -За (2уах 3a dy dx x2 4a by changing the order of integration.

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Q: To integrate x3x² dx' Ox хех2 242 x² OX we apply integration by parts and in the form u dv, dv is…

A: We have to determine the integral

Q: To integrate 3x² e4² ΟΧ dx' we apply integration by parts and in the form u dv, u is set as:

A: ∫x3ex2dxTo do integration by parts we have to get it in the form ∫fg'

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

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Q: Evaluate the definite integral. 10x dx 19+5x2 Select one: OA. - 2 1 + 6 B. 14 2 2 C. VT - 3 D. 2/T -…

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Q: Which of the following uses integration by parts? (1) fxcos.x°dx (3) fxlnxdx (2) [x'e*dx - In x dx…

A: we have to find the integration by parts from the following

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, dv is set as: O ex dx O…

A: We have to find the dv

Q: Use the formula f f(x)g (x)dx = f(x)g(x) – S f (x)g(x)dx for the integration by parts, and Integrate…

A: Use the formula which is given in the question.

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

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Q: Use the indicated substitution to evaluate the integral.

A: we have to use the substitution x=3secθ to evaluate the integral ∫dxxx2-9

Q: State ALL the theorems on integration used in the following computation: 2 2 (32- 3 d - 23 3 3 -0) –…

A: Remark: The sum rule of integration is  ∫ ( f ( x ) + g ( x ) ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x.…

Q: In'(r) da. integration by parts (a)

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Q: c) Calculate the integration Y+1 dydx

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Q: Write the iterated integral ∫10-10∫200 (x2y + 2xy3) dy dxwith the order of integration reversed.

A: To evaluate: ∫-1010∫020x2y+2xy3dydx. Evaluating the integral.…

Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: 6. Change the order of integration and evaluate the integral (**2y+1 dxdy. r+1

A: ∫01∫0y+4 (2y +1)dxdy/(x +1) now change the order of integration ∫0y+4∫01(2y +1)dydx/(x +1) ∫0y+4[(y2…

Q: To integrate x3 ex2 x " 0x we apply integration by parts and in the form u dv, dv is set as:

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Q: Use integration by parts to evaluate: xe2x dx DA. 2e2*(x – 2) + C OB, x²ex² + C OC. -[2x – 1] + C 4…

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Q: Solve the integral equation f(x) cos Ax dx = e. %3D

A: Given integral is, ∫0∞fxcosλxdx=e-λ The right-hand side is a Fourier cosine transformation function…

Q: In each part, confirm that the formula is correct, and state a corresponding integration formula.…

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Q: Which of the following uses integration by parts? (3) fxlnxcx In x dx ... (1) fxcosx'dx (2) fre*dx…

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Q: Find an integrating factor. (6x3y + 2xy + 2y³) + (x2 + y?)y' = 0 µ(x) : Solve the giv en equuation

A: Concept : First we have to check given equation is an exact differential equation or not. If…

Q: Evaluate the given integral. 1 a) dx ² +x – 2 3 b) dr 3 – 9x2

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Q: The integration A. 114 Β. π C. 0 D. 1/2 Z|7 sinc(4nt) dt has the value (hint:use the FT)

A: Given integral is ∫−∞∞sinc4πtdt. We have to evaluate the given integral. Here, ft=sinc4πt. Now, for…

Q: a) Solve the integration by parts [cos(x)e*dx.

A: We need to solve the given integral  This can be evaluated as follows:

Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: Q1-Evaluate the integral 2х — 5 dx - х2 — 5х + 1 3

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