Find each antiderivative using Table 1. 1 -dx 81 dx 19. 20. x(7 - x)

Q: s dx x+√2x+1

A: Let  2x+1=u ⇒dudx=12x+1 ⇒dx=2x+1du also x=u2-12  ∫dxx+2x+1=2∫uu2+2u-1du…

Q: Differentiate. y = In [(x + 6)* (x + 7)® (x + 3)5] d [In [(x +6)*(x +7)® (x + 3)°]] = ] dx

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Q: cln10 pIn10 4sinh² (x/2)cosh(x/2)dx

A: Given that a finite integration and we solve this integration by using general formulas of…

Q: Use U substitution. to. find. each antiderivative (x²+5x+1)" dx

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Q: S(3x2 + 2) V4x³ + 8x dx

A: Solving the problem by the criteria of integration.

Q: 5.S dx 2 x+5

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Q: iate ſ In(x + v1 +x²)dx

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Q: Find each antiderivative

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Q: 2x2 dx 1-x3

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Q: Integrate by subsitution 3. S(5+ 2x + 3x²)(2+ 6x)dx

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Q: Integrate by substitution. 2 [x²(x³ +5) dx

A: Given query is to find the integral using substitution.

Q: integrate: [e^(2x)]cbrt(e^x +2)  dx

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Q: Approximate 3 (x – 5) dx 0. using 4 rectangles, and right endpoints of each subinterval.

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Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Q2 _Calculate the integration (a) |(5x2 – 8x + 5)dx

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Q: 1. Sx³dx dx 2. S

A: In integration we basically have definite and indefinite integrals . In definite integral we have…

Q: Perform the following integrations: 9. 10. dx

A: To evaluate the given integral.

Q: 5. S Vx In 2x dx

A: I= ∫x ln 2x dx   =∫ln 2x x ln 2x dx   = ln 2x∫ x  dx- ∫ddxln 2x∫x ldx dx   = ln 2x x3232 - ∫22x…

Q: Integrate: S Зx?+x-8 dx x3+4x

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Q: S4x(5x³ – 3x)dx

A: To find the antiderivative: ∫4x5x3-3xdx

Q: cosh(lnx)dx 4. f 5. [* cosh vxdx 6. Jo Sm 10 4sinh? () cosh ) dx

A: Solve the three questions.

Q: Find each Antideriva (x200 dx S Vx dx 1 dx X4

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Q: evaluate using Integration by Parts, substitution, or both if necessary.

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Q: |(181? +t+2) dt dx 8.

A: Given expression is

Q: d х [S* dx] Vx² + 2x dx

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Q: Find the most general antiderivative. 20) [7x3 - 4x + 5)dx

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Q: Vx2 - 64 dx

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Q: x2 dx V4 – x2

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Q: 1 :dx J xV16ln² x – 9

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Q: 4. x³+2x+2 2 x²-1 dx

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Q: (x³+3x) dx x3+1

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Q: Evaluate. (Assume x>0.) Check by differentiating. x* In x dx

A: Given,          ∫x4lnxdx

Q: (2x4 + 3x² + 7) dx

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Q: | (x³ +3x? -x+3) dx

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Q: (e 2X Integrate 2X to dx

A: The given integral is ∫e2x+1xe2x-1xdx   Formula used: a2-b2=a+ba-b

Q: 3 dx xV9- (In x)2

A: Let's find.

Q: 4. S V4x –1 dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 6. dx Vx - 1

A: Given that I=∫161x2-1dxsolution…

Q: Evaluate and simplify. L dx 1 V1-2x-x²

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Q: (e) ſx(1 – x)99 dx

A: solution is given below

Q: what chorces for 4, dv simplify, will x In Cy) dx vsing integrat by parts lON

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Q: Find each Antiderivative: (x200 dx e) ƒ = dx

A: Basic integration Formulae,∫xndx=xn+1n+1  ----(1)∫a dx=ax where a : constant  ----(2)∫eaxdx=eaxa…

Q: Explain geometrically (without calculation): x/n dx = 1 x" dx + (for n > 0)

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Q: Evaluate the integral. (x² + 6)e dx X- 3.95

A: As per given question We have to defind integral

Q: d. X 3 Vt4 + 1dt dx -x

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Q: Q2- Evaluate 1- L,(x + 2)*e=x+2)dx.

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Q: 5 |V25 – x² dx Compute the value of

A: Given: I=∫0525-x2dx we know that ∫a2-x2dx=x2a2-x2+a22sin-1xa+c                                  ...1

Q: Find the most general antiderivative. 20) [(3x³ - 8x +2)dx

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Q: 4x V x4 + 13 dx =,

A: Given: ∫4x3x4+13dx