1. (a) Without using a calculator, determine the following integrals: 8.x dr3; (1) 2+8r- 9 (1)/ (ii) dr. r2 + 8x +41

Q: Evaluate the Integrals: ∫ (2x2+3)dx/x(x+1)2

A: Given the integration I=∫2x2+3x(x+1)2dx

Q: How to evaluate the integral of [(dx)/(9-x2)(3/2)]

A:

Q: I. Find the following integrals. – 8x +5)dx 2. [(-6x' +9x² + 4x - 3)dx 1.

A: 1. Consider the given integral. I=∫5x2-8x+5dx

Q: Use any method to evaluate the integrals

A: Since you have posted multiple question we solve first question for you  To get the solution of…

Q: 6. Estimate the integral: ܐܢ ex. dx

A:

Q: How would I evaluate this indefinite integral?

A: Consider the provided indefinite integral,Simplify the given indefinite integral as follows,

Q: 6. Evaluate the integral ex e* +e-xdx

A:

Q: 14 Find the integrals using integration by parts. Lx(x + 4) dr --2

A: Given that:(a) ∫x(x+4)2dx

Q: Evaluate the integrals

A:

Q: The result of the integral is equal to 4 √ = (x − 1)(x + 1) dx

A:

Q: 2 x ln((2x)²) dx 1

A:

Q: 5. Write down an integral that can be solved by usingintegration by parts with u = x and another…

A: dv=x dx

Q: 1. Evalute the improper integral 3x dx. 1+ x2

A: Given: ∫-1∞3x1+x2dxTo evaluate the improper integral:

Q: S 8-3x (x+1)(x² − 4x+6) - dx

A:

Q: dx (1 – x3

A:

Q: 34. x sec xdx

A:

Q: Evaluate the integrals ∫dx/1 + (3x + 1)2

A:

Q: What are the two general ways in which an improper integral may occur?

A: Type 1:  An integral is said to be improper if its lower limit of integration, upper limit of…

Q: dx (apply the properties on how to solve improper integrals 1 – x²

A: Given query is to find the value of the integral.

Q: Evaluate the integrals in ∫ln x dx/x√(ln2 x + 1)

A: Consider the following integral: ∫lnxxln2x+1dx=I Substitute ln2x+1=u→2lnxxdx=du in the above…

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: Evaluate the integrals

A: Given integral to evaluate ∫-44xdx The modulus  function is given by  x=x        if x≥0-x    if…

Q: [x² In x dx

A:

Q: =dx V2x* +3 4

A:

Q: In x (7) Í dx (8) dx 4 4+x (9) [xVI-2x dx

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Evaluate the integrals using the substitution method of e8x dx

A: To evaluate the integral: ∫e8xdx Solution: Let substitute t=8x. Differentiating both sides, we get…

Q: Evaluate the integrals.

A: The given integral is ∫022x+13 dx. Evaluate as follows.

Q: 3 1 L₁ dz -3 (x+2) ³0 Compute the integral:

A:

Q: Find the integral 13x³ + 6x² + 7x + 2 dx= (x + 1)²(x² + 1)

A:

Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: Evaluate the integrals. ∫ex + ex dx

A: Let,                 I = ∫ex+ex dx  = ∫ex.eexdx          (By exponent rule)   Now to find this…

Q: 4. Evaluate the integral: In6 -2x + sinh 2x|dx e2x + e-2x

A:

Q: I need help solving the integral of the problem below.    ∫(√x+∛x)dx

A: Given integral can be written as

Q: Evaluate the integral (x – 1)ez xp- x² – 2x + 2

A: The objective is to find ∫-∞∞(x-1)eix(x2-2x+2)dx It is known that, eix is an increasing function.…

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

A:

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: S 3x+1 -dx x²-x-6 2

A: We know, ∫ dx/x = ln|x|

Q: In -dx x²

A: This is a problem of integration. Based on the general formula of integral by parts we will solve…

Q: Select the basic integration formula you can use to find the indefinite integral. 10 dt (10t – 3)2 +…

A: Given that              ∫ 10/{(10t - 3)2 + 81} dt Here we have to find the indefinite integral by…

Q: In x dx .2

A: We need to solve the integral.

Q: 3. Evaluate the integrals: -2 4x2-2x+1 а. -1 b. dx 1 х

A: 3. We need to evaluate the value of the following integrals a.  ∫-124x2-2x+1xdxb.  ∫1e1xdx

Q: 5 1 1o ( 125 + 25x + 8) dx 6 1 X So (1 + x²)³dx 3 1 √ dx 1+x²

A: Given :∫05x2125+125x+e6dx∫01x1+x23dx∫11+x2dx

Q: find the complete integral for equation  p2-q+y2-x2=0

A: Answer

Q: Evaluate the integral of ex*+1 2x dx.

A:

Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: Ĵ3xco0s(4–x²)–8xV4-x° dx

A:

Q: (3x+5) dx x3 –x² –x+1

A: Consider the provided question,

Q: х — 3 (x+ 2) (x – 1)²

A: The given integral is; (x-3)/[(x+2)(x-1)2].

Q: 5a) 1 x[In (2x)]3 S.₁- -dx 5b) X ² (x² - 4)" S₁²7 3/2 dx

A: We have to evaluate the given improper integral. Here we will use the following formulas-…