–1/2 | (x (x² + x) + 4)dx.

Q: xsin-1x > [4) S*s dx [4] S Y1-x2

A: Here is the solution

Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

A:

Q: Find dy dx 2 for x²exy = 5 WA/

A:

Q: S(x - 2x –1)dx – 2x-

A: In integrate by using formula for general case.

Q: x²(In(x))² dx

A:

Q: [2 f(x)dx= 10 If then equals ?

A:

Q: Sla 1 z dx |(25 – x²)3/2]

A:

Q: 4. S dx 9-x x2-1 dx 5.

A:

Q: Solve th D.E using Exact -(3x² – 6.xy)dx +(-3xr' – 2y)dy = 0

A:

Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: dx 1- S 4+x2

A:

Q: 2dx x (3(ln x)2 + 12 In r – 15)

A: Indefinite Integration

Q: x+7 dx. egral: | x² - x-2

A: To find the integration

Q: (a) S v16 – 9x²dx using th - (b) dx using thes V9-x2 dx using the subs

A:

Q: Find S dx √X²-2x+1

A: ∫1x2-2x+1dx=∫1x-1dx=lnx-1Add a constant to the solution=lnx-1+C

Q: a. S f (x² - 2x + 1) e²x dx

A:

Q: Q2: Fill the blank: 1) lim (1+)5x x48 4x 2) lim x.e-3x = X-8 3) (csch-¹x³) = = 4) ₂° e-*dx 5) S-…

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Q: x(x²-x+2) dx is equal to 3

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Q: -1 | In(-x)dx -7

A:

Q: Q3. Find dt 4x – 2 dx x² + 20 4t

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Q: Find the formula for df-1 /dx. f(x) = (1 – x)3 1 O A. 3x2/3 О В. 1-х1/3 Ос. -3(1- х)?

A:

Q: -1)/(x4))1/2

A:

Q: 1 The value of f|5x – 3|dx is

A: Integration of the absolute valued function

Q: y = In [e x (x° +2) (x³ + 8x)] d [In [e 6x (x5 + 2) (xS + 8x)]] =] dx

A:

Q: In(x²) dx 1

A:

Q: In the function given. Evaluate the integrals.

A: ∫36-3gxdx=∫36-3dx·∫36gxdx Also, ∫36gxdx=1

Q: dx is is equal to: 2x/4-(2x)2

A:

Q: For y = 5x2 + 10x – 3, find dy at x = 2 if dx 0.1. -

A: The given function is  y=5x2+10x-3

Q: х — х* - 3х - 2 X | dx x* - x'+ 4x – 4x 3

A:

Q: 5x-3x 4) lim x→00 7x2+1 d 5) [In|sin x|] dx d 6) (x³e*]

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: 5 (a) | x² In(2x) dx (b) x'e*dx 'xp, Jo

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Q: (#9) S x2 dx V16-x²

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Q: If f(x)=3^x x^3, what is dy/dx?

A: Solution: Here  f(x)=3xx3

Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

A:

Q: x*dx 3. S x2-1

A: use a partial fraction to solve the integral.

Q: dx 1) S- x2-2x+1

A: As per the guidelines we can only solve one question post other question seperately. Formula used  ∫…

Q: Compute dx. x2 + 4x + 8

A: Our Aim is to compute the integral given below:-∫02 xx2+4x+8dx -(i)

Q: In(x) dx 4

A: we know that, intergration of ln(x) = xln(x)-x Also d/dx (ln(x)) = 1/x integration of 1/x = lnx

Q: 1 T/ -dx 6 x²+16

A:

Q: If ƒ x Inx dx = x² In x – S f(x)dx, what is the value of , 4f (x)dx?

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 1 вхось xа(1 — x)bdx - = 6xº1 Bx®1 - x)dx /0

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Q: B4. Evaluate the integral [(3x² - ª ++5 x -6) 4 +5 /x – 6) dx .

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Q: 2. Find b such that dx 1+x2 3

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Q: iv) L,x²e=* dx -2 -3x dx 1

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Q: iii) So z dx 1+x2

A: Given: ∫01 x1 +x23dx To Evaluate given integral Proof: We will evaluate the given integral by…

Q: 2x +1 S- dx x(x² +16)

A: Find the integral by partial fraction

Q: x+3 k) S- dx x2+6x-11

A:

Q: (2) √ 2²² dx S 9-x² (2) > fx(x + 1)¹ dx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture and a…

Q: If y = (6x + 7)0.5(2.6x2 - 1.9), what is dy/dx?

A: