Find the indefinite integral∫ ln √x / x dx

Q: 1 dx. 3 Evaluate x(lnx 8.

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Q: Evaluatelimx→1(ln x)/(x - 1).

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Q: 10. x*(lnx + 1)8** dx

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Q: _2] ln(1+x)

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Q: So 1 x²+7x+10 dx

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Q: S; 2 dx x(3(Inx)"+\지lnz-15)호

A: We use substitution method to solve this integration

Q: dx x (In² x – 6 ln x + 10)

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Q: Differentiate   y = 3(ln x/x)

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Q: 1 dx x[9+(ln 3x)" 8.

A: use simple integration method.

Q: Differentiate   y = (ln x)2

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Q: 10 logio (10x) dx 1/10 X

A: This question will be solved as follow-

Q: Solve the equation for x.   4 - ln x = 0

A: Logarithm and exponential functions are inverse of each other. According to the logarithm and…

Q: d Find -(3 ln(x)) dx

A: To find: ddx3lnx

Q: Differentiate   y = ln(x2 + 1)/(x2 + 1)

A: We have the given function as y=lnx2+1x2+1        ⋯⋯1 We know that, for two differentiable function…

Q: csch(ln x) coth(ln x) dx

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Q: Calculate y'. y = ln(x ln x)

A: Given: y=lnxlnx Chain Rule for Differentiation: ddxf gx =f'xddx gx Product Rule of Differentiation:…

Q: Differentiate   y = (x3 + 1) ln(x3 + 1)

A: Given, y=x3+1 lnx3+1

Q: Differentiate y = ln ( x 3 + 1 )

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Q: So 1 x²+7x+10 3ln 2-ln 2 dx

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Q: e8 dx x/ln x ||

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

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Q: Find an approximate value of 8. [6x 6 x dx

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Q: Solve for x : Inx+ln 3=2

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Q: 2dx x (3(ln x)2 + 12 In r – 15)

A: Indefinite Integration

Q: 3 dx x(ln(x))³

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

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Q: (2+ln? x) -dp- x(1-In x)

A: Given integral, ∫2+ln2xx1-lnxdx

Q: Explain why ln x is positive for x > 1 and negative for 0 < x < 1.?

A: Plotting: y=lnx

Q: Find the antiderivative of 2x((ln(10x))2

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Q: 3 dx VT (x + 1) x) x

A: Given ∫13dxx(x+1)Substitute u=x→dudx=12x→dx=2xdu=2∫1u2+1du

Q: find x ln x dx

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Q: Find (²-1) ln(x)dx

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Q: 10. y=ln(x² +3}) %3D

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Q: 3. S x² ln xdx

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Q: Q5// Evaluate *x5*(1+ln x)dx.

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Q: 13. Find the extrema of f (x) = 2x² ln x – 11x?.

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Q: What is q′(x) when q(x)=ln((x^2+1)(x^3+x^2+2))?

A: We first separate the log using the product rule of log.…

Q: What is the antideravative of  (1/ln2) 1/x dx?

A: Given,

Q: (2+ln æ)* dx 3

A: Given∫2+ln x3xdx

Q: 1. S(x* - 5)'x² dx

A: According to our guidelines , we can answer only first question . Kindly re-post other remaining…

Q: If h(x)=ln(6x+4x53sinx), find h′(x).

A: use the chain rule of derivative and simplify the result.

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: 1 dx Evaluate -Ln(x)

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Q: 4. coth(ln x)

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Q: х —1 18) y=ln. Vx+1

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Q: Solve for x: ln(x+1) - ln(x-1) = 1

A: Given : ln(x+1) - ln(x-1) =1

Q: V1 - (In x)² x ln x VI dx

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Q: 1ln(1 + x) dx X 0

A: We have to integrate

Q: 1. S x(x2022+1) dx

A: The given problem is solved below in detail.