Evaluate the integral. r1 x3 - 2x – 10 dx Jo xt — х — 6

Q: Evaluate the integral (2æ + 6)(x² + 6x + 9)*dx by making the substitution u = x? + 6x + 9. + C

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Q: Evaluate the integral by making the given substitution. Sx x +2 dx, u = x³ +2

A: The given integrand is  x2 (x3+2)1/2

Q: 2x Evaluate the improper integral J da, if it exists. (z² + 121)?

A: Use the substitution method of integration

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

A:

Q: Find the integral ∫(1/t2i+1/t3j+tk)dt.

A: We first separate the integrals

Q: Substitute u = x + 2 into ul0 - 2u° + C to evaluate the given integral in terms of x. 10 | x(x + 2)8…

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Q: dx Evaluate the given integral: Jo 5-ex

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Q: Evaluate the integral. T/2 9 cos?(0) de

A: Integration of 9 cos2(theta) from limit 0 to π/2.

Q: 2x Evaluate the improper integral J dx, if it exists. (x2 + 64)2

A:

Q: Evaluate the iterated integral: , (2x²y + 3xy*) dr dy.

A: Given the iterated integral             ∫-12∫242x2y+3xy2 dx dy Evaluate it.

Q: Evaluate the improper integral: dx x In(x) а) 012 b) 02 c) Odiverges d) 01 e) 06

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Q: (a) Evaluate the integral using the substitution u = In (5x). x In (5x) dx x In (5x) ? Edit +C (b)…

A: An integral in some cases can be simplified using a substitution. For example ∫ln(x)xdx with the…

Q: Evaluate the integral: rV1+ 25 /1+ 25z°dz + C

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Q: Evaluate the integral f 2x (x? + 1)“ dx using the substitution u = x2 + 1.

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Q: * (Find the integral of e^2x c

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Q: Evaluate the integral. (Use C for the constant of i 4x2 + 3x + 4 dx (x² + 1)2

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Q: Evaluate the integral J 2x(x² + 6)¨ dx using the substitution u = x2 + 6. | 20 (a? + 6) " d.x +C

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Q: Evaluate the integral using the given substitution. 18(6x- 2)6 dx , u = 6x - 2 0.(6x - 2) +C O (6x -…

A: The given integral is ∫186x-2-6dx and  u=6x-2

Q: evaluate the iterated integral.

A: ∫03∫-20(x2y-2xy) dy dx

Q: 2 Væ? – 1 -dx. x² 1

A: Here , we will solve the integral using substitution form .

Q: Evaluate the integral by making the given substitution. dx u = 7x + 4 (7x + 4)3 + C

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Q: Evaluate the improper integral: dx b) Odiverges c) 14 d) -4 e) 8 a)

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Q: Evaluate the integral f 2x (x? + 5)° dx using the substitution u = x2 + 5. 2x (x² + 5)° dx +C

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Q: Evaluate the improper integral: 17 dx a) O-17 b) Odiverges c) 17 d) O34 e) OV17 8 8.

A: Given integral is ∫-∞∞17x2dx. Adjust integral based on undefined points. There is undefined points…

Q: Evaluate the integral using the given substitution. dx ,u = 6x + 1

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Q: Evaluate the integral using the given substitution. Sx4x5 -s;² dx , u =x5 -8 * - 8) + C

A: We have to solve given integral by substitution.

Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: Consider the following integral: 1 1 I = 2ey? dyd: 0 x

A: Given: ∫01∫x12ey2 dy dx

Q: Evaluate the given integrals. 1. ſ cos v2x dx 2. fx a*dx

A: Please see the answer below.

Q: Evaluate the integral f 2x (x² + 2)° dx using the substitution u = x? + 2. | 20(a* + 2)" de +C

A: The given integral is: I=∫2xx2+26 dx

Q: Evaluate the integral *(2* – 3)*da a* – 3)' by making the substitution u = x* – 3. | +C

A:

Q: Evaluate the integral f 2x (x² +1)** dx using the substitution 14 u = x² + 1. | 20 (a² + 1)“ dx +C

A: The given integral is: I=∫2x(x2+1)14dx Substitute u=x2+1 After differentiating,…

Q: We now use the substitution u = x° + 8x and du = (9x° + 8) dx to convert the entire integral into…

A: We have to solve integration

Q: 2dt t/4t4 – 1

A: Evaluate: ∫2dtt4t4-1

Q: Evaluate the integral. x² cos(3 x) dx =| + C

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Q: Evaluate the integral, then find 1- 3a. w – 1 dw - = w + a ln (w+ 1) + C w + 1

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Q: evaluate the triple iterated integral.

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Q: 1 dz c+x2 c)

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Q: 11 dx Evaluate the integral: , (5æ+6)² 11 55

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Q: Find the integral t3 dt 28 + t8 +C

A: The given integral is ∫t328+t8dt

Q: b) Evaluate each of the following integrals: 2 i) | cos(2x)dx, 4x3 -dx. 1+ x* ii)

A: Explained below

Q: Evaluate the integral. 13 dx 1 O A. 0 О В. - 13 13 Oc. -ze? O D. 13

A:

Q: Evaluate the following integrals. i) S Vỹ+ + edy i) /x Vx? – 1 dx x+2 dx x2+4x-2

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Q: ii) Evaluate the integral // Va? + y°dxdy. 1-y2

A: Find your answer below

Q: Find the integral. dx O A. 5x e* - In |x| +C O B. 5e* - In |x| + c 1 О с. 5ех. + C 2x? 2 O D. 5eX +C…

A: The solution is :

Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

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Q: Evaluate the iterated integral. 6 r8 × Jo Jo (x + y) dy dx

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Q: Evaluate the integral.

A: Evaluate the integral.              ∫04-x2x2ydy

Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below