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

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A: Topic = Integration

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A: Given: ∫121dxx2x2+4

Q: Evaluate the integral.

A: Given integral is We will use the following substitution to evaluate the integral.

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Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

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Q: Use the indicated substitution to evaluate the integral.

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Q: Evaluate the integral. 2 5 dx VE x²Vx² – 1 .2 - NOTE: Enter the exact, fully simplified answer.

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Q: Use the substitution formula to evaluate the integral. T/8 19) (1 + etan 2x) sec 2x dx

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Q: Evaluate the integral. 2х + dx J1

A: We have to evaluate the given integral.

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A: Given integral to evaluate ∫14x249-x2dx=14∫x249-x2dx substitute u=sin-1x7x=7sinudx=7cosudu The…

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A:

Q: evaluate the integral.

A: then integrate by substitution

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A:

Q: Evaluate the integral. 1 -dx (x + 8)(x² + 9)

A:

Q: Sx²e2x*dx `x²e?

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Evaluate the integral. 0.6 x2 dx V 9 - 25x2

A:

Q: 2 Væ? – 1 -dx. x² 1

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

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Q: Evaluate the integral

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Q: x-3 dx r³+9x +9.x

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Q: Evaluate the integral using an appropriate substitution. dx = +C x√√8-xd

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Q: Evaluate the integral v22 -6x? dx V1- x2

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Q: 2r cos x dx

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Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: 4 + V16-x? dx 3 2

A:

Q: 2x dx J (x² + 15)2²

A:

Q: Evaluate the integral 6 dx (x+1) (x2+4)

A: Given,

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A:

Q: evaluate the integral.

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Q: Use substitution to find the general integral (x-4) *dx x²(x- 4) $dx = %3D |

A: We have to find the integral

Q: Use U-Substitution to evaluate the indefinite integral. S(5x + 2)?dx S 2x sin(x²) dx

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Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: Evaluate the indefinite integral: dx + C. %3D 6x4

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: Evaluate the integral. dx 2 (a² + x²)3/21 a>

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Q: find the indefinite integral 2x dx J (x² + 15)22.

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Q: Evaluate the integral. 'T/3 3 tan5(x) sec (x) dx

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Q: Evaluate the indefinite integral. x2 dx V0.2x3 + 2.7 + C

A: The query is to find the value of the given indefinite integral: ∫x20.2x3+2.7dx

Q: Evaluate the integral (2х — 8)dx - x2 – 6x + 18

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Q: Evaluate the integral 2x (x2 + 3)° dx using the substitution 6 u = x + 3. | 2.x (x² + 3)° dx +C II

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Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Evaluate the integral. B 4х- 3 dx J2

A: To evaluate:

Q: Consider the integral 3 x2 dx 81- r /2

A:

Q: Evaluate the integral: 1 dx = %3D x2 – 20x + 101

A: I=∫1x2-20x+101 we use the common formula ∫du1+u2=lnu+1+u2+C

Q: Evaluate the integral: x2 dx V1 - x6

A: Given integral is: ∫x21-x6.dx