Evaluate the indefinite integral: 2x² Vx³ + 5dx Note: Maintain fractions if applicable.

Q: Determine the integral by making an appropriate substitution. Sa7-21990x6 - 125) dx O 7x6 - 12x5 + C…

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Q: Evaluate the integral using an appropriate substituti NOTE: Enter the exact answer. x²e-&g³ dx = +C

A: Given that: ∫x2e-8x3dx

Q: Use properties of the indefinite integral to express the following integral in terms of the simplest…

A: Use the following property of indefinite integral: ∫fx-gxdx=∫fxdx-∫gxdx∫kfxdx=k∫fxdx Consider the…

Q: Find the integral. [col³ (x) csc ³¹ (x) dx (Use symbolic notation and fractions where needed. Use C…

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Q: Evaluate the integral. r0.75 x2 dx 9 – 16x2

A: We apply trigonometric substitution and change the limits and the values as shown below.

Q: Evaluate the integral by any method. NOTE: Enter the exact answer. V6 dx 3 + x4

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Q: Use substitution to find the indefinite integral. 6 10(1

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where dx Vx2 + 6

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Q: x3 dx 1-x2

A: Topic- Integration

Q: Evaluate the indefinite integral. 4x3 da (x4 + 1)? + C

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Q: Evaluate the integral 34 dr, by making the appropriate substitution: u = 5) da- 34 NOTE: Your answer…

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Q: Evaluate the indefinite integral. 26 x14 xp= 3 arctan(1) – 3 arctan(0) 2 X + C

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Q: Write the integral as a sum of integrals without absolute values and then evaluate. 1 = ["² - 1|dx…

A: From the given problem: I=∫06x2-1dx From the property of modulus function, x2-1=-(x2-1)  if…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8. dx : (1 –…

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Q: Evaluate the integral. -0.8 (x -208) da

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Q: x7 +1 dx = x8 + 8x Vr8

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Q: Evaluate the indefinite integral. 3 16 +x2 dx (x² + 16) 48x + C

A: The objective question evaluate the indefinite integral.

Q: Evaluate the integral. dx x216x + 65 NOTE: Enter the exact answer. + C

A: Given ∫dxx2-16x+65 Use the following formula to evaluate the integral, 1x2+1dx=lnx+x2+1

Q: Evaluate the integral. 0.75 x2 dx 9 – 16x2

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Q: Evaluate the integral. -2x x2 NOTE: Enter the exact answer.

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Q: Evaluate the improper integral. (Use symbolic notation and fractions where needed. Use the symbol o…

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Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: 0 ✓1+13xdx

A: Given that ∫021+13x3dxSolution:let 1+13x=t313dx=3t2dtdx=3t213dtat x=0,t=1at…

Q: Evaluate the integral. 14) x6(x7 - 6)4 dx

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Q: Use properties of the indefinite integral to express the following integral in terms of the simplest…

A: The given integral is ∫(5x^2–5x) dx.It is known that, if f and g are integrable functions, theni) ∫a…

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the const |(* +…

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Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

Q: .3 2х — 3 -dx 4 x –x

A: First break the given Integral  Then take 4x- x^2 = u and in other one complete the square  Finally…

Q: Evaluate the indefinite integral. -1 x2 = xp 21 (x²–7)5/2 (x² – 7) * Remember to use capital C.

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Q: Use substitution to find the indefinite integral. 6x+7 (3x +7x) to

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Q: Evaluate the integral by any method. NOTE: Enter the exact answer. d.x V4 - 3x16

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Q: Write an integral expression which is equiralent to the following but with the order of intergration…

A: First we should graph the region for better understanding

Q: Evaluate the indefinite integral: J 12x2 –16x dx 2x³ – 4x² +7 Note: Maintain root symbols if…

A: To evaluate the below integral. ∫12x2−16x2x3−4x2+7dx

Q: Use substitution to find the indefinite integral. 4x+7 xp- (2x? + 7x)°

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Q: Use properties of the indefinite integral to express the following integral in terms of simpler…

A: Given:The indefinite integral is ∫(−7x2 +2x+6)dx.

Q: Use properties of the indefinite integral to express the following integral in terms of simpler…

A: Use the sum rule and spilt the integration.

Q: Evaluate the indefinite integral by using the substitution u = 5-x' to reduce the integral to…

A: Given the integral

Q: Evaluate the integral. 0.75 x2 dx 9 - 16x2

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Q: Calculate the integral. (Use symbolic notation and fractions where needed.) - sinh(15x) dx = +C

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Q: Calculate the integral. (Use symbolic notation and fractions where needed.) - sinh(9x) dx

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Q: Find the indefinite integral using trigonometric substitution ∫(7dx)/(sqrt(x2+9))

A: I=∫7dxx2+9x=3tan⁡θ⟶θ=tan−1⁡x/3dx=3sec2⁡θ⋅dθI=∫(7)(3)(sec2⁡θ)dθ(3tan⁡θ)2+9I=∫721 sec2θ⋅dθ3sec2⁡θ

Q: Evaluate the improper integral. -64 dx V64-x

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Q: a+bx² √3ax+bx³ dx

A: This question is related to indefinite integration, we will solve it using given information.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (18x – 17)°…

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Q: Evaluate the indefinite integral. 8x7 dx (28 + 1)² + C

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Q: Evaluate the integral by any method. NOTE: Enter the exact answer. dx = /4 – 3x8 --

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Q: ここXP x(メャッ)。

A: put x^2+7=u so that 2x dx=du .and solve the question in 2nd step.

Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: Evaluate the indefinite integral by using the substitution u= x2 +11 to reduce the integral to…

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Q: Evaluate the definite integral. Use "u" substitution when appropriate only! 5. (3x - x2

A: Integral Question

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.