1 3 ln(2.r Evaluate dx.

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A: The second fundamental theorem of calculus states that if f is continousmapping in [a,b] and F be…

Q: |In². |In? x – 4 ln x – 5| dx. Evaluate - e-3

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Q: 2 -5x dx e EVALUATE 4(1 – ) (1 - ) | None {(5 –)

A: To find integration of followingI=∫02e-5xdx

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A: Since you have submitted two questions, we'll answer the first question. For the second question…

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A:

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A: Note: We are entitled to solve only one question at a time. To Evaluate: ∫1x1+x2dx

Q: 35. G(t) = sinh(In t) %3D

A: We have to find derivative

Q: |In²r - |In? r – 4 ln r – 5| x – 4 ln x – 5| dx. Evaluate -3

A:

Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

A:

Q: 4. § dx – dx x In x

A: Given 1. ∫5exdx2. ∫(2-3ex)dx3. ∫72x+3dx4.∫1xlnxdx

Q: 13. [" e*dx

A: Use integration rules

Q: S csch-x coth x dx

A:

Q: 3) Evaluate for ln(x + 1)dx x

A:

Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

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A:

Q: True or false? As x→ ∞, ln (x) = o(ln (x2 + 1))

A:

Q: 2 0.07x dx Calculate 330e

A: We have to calculate the integral ∫02330e0.07xdx.

Q: (a) Evaluate dx. xVx* +1

A:

Q: 9. Evaluate et dx 1+e*

A: Consider the provided integral, ∫ex1+exdx Evaluate the provided integral. Apply the u-substitution…

Q: 1. S 5e*dx 2. S(2 – 3e*) dx

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Q: 5. y ln x – x In y = In e2×

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Q: Ln (+x) dx

A: Given integral is ∫ln (x2+x) dx=I (say) We will do this by method of by parts.

Q: |In² x – 4 ln x – 5| Evaluate - dx. e-3

A:

Q: 1 dx = e^+ 4 e

A: I=∫1ex+4e-xdx =∫1ex+4exdx =∫exe2x+4dx Now, assume ex=t⇒e2x+4=t2+4 by taking derivative, ex dx=dt

Q: 2x+ 17 3.5 dx x* +6 4. ſ cot63x dx

A:

Q: 2) S exp(ln(2)2*)dx

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Q: .3 +1) dx

A: Integration of x3/4+1 is x(3/4)+1/((3/4)+1)+x

Q: 1) 3 )dx

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1 dx O (1+ x)1/4 1.

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Q: e dx S- 2x – 1 e

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Q: Dx (Inlyl) = Dx ( In 121 + +an (3x) • Inx + x³ In e - In | In x |

A:

Q: a+3 Use Ar = 0.5 and a left-hand sum to estimate xe* dx.

A:

Q: (e 2X Integrate 2X to dx

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

Q: 10 Find 5e"dx Answer = (round to two decimal places)

A: ∫2105exdx

Q: (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that…

A: The solution is given as

Q: dx Evaluate e x(Inx)3

A:

Q: •e ln x dx 1

A: ∫lnxx dx lnx=t⇒1x=dtdx⇒1x dx=dt Therefore, ∫lnxx dx=∫t dt=t22+C=lnx22+C

Q: 2х + 10 dx Evaluate 2(x – 4)

A: topic - indefinite integration

Q: 1 +et+10 + 4* + x – 5 dx - + xA

A:

Q: 10. dx 11. xe*dx 1 ST

A:

Q: Find and explain the error in the following Z 6 0 1 x − 3 dx = (ln |x − 3|)   6 0 = ln |6 − 3| −…

A: Integral evaluation

Q: х —1 18) y=ln. Vx+1

A:

Q: e e (lnx)³ dx X

A:

Q: Va(ln(x))² dx

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate

A: Given, ∫02x1+e-x2dx Now substitute, -x2=t⇒-2xdx=dtx dx=dt-2 Now, if x=0 ⇒t=0if x=2⇒t=-4

Q: 4. S dx – dx x In x

A:

Q: 4 Vx? +15 ² +15 dx Vx* +3 4 ! 1 dx Jx' +x° ,5 3 ,5 x° +x'

A: Please see the below picture for detailed solution.

Q: is equal to A Inr+ B ln s where A = and where B =

A: Given expression :