Suppose we perform the substitution .3 u=9-x in the integral

Q: 3 4 dx x2 + 9

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Q: Evaluate the integral. | a sec"(3z) dr =| + C

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Q: Evaluate the integral. 3. (In(x))² x3 dx 1

A: I am attaching image so that you understand each and every step.

Q: -s(-+)( + }) 1. dt

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Q: Evaluate the integral. 8 dx 3 1

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Q: Evaluate the ff. integrals using substitution: dx 1. S (5-2x)2

A: 1. Using substitution u=5-2x

Q: Evaluate the integral of e^(2lnx)

A: We simplify  e^(2lnx) first.

Q: @ evaluate the indefinite integral fxº ex* dx

A: Given problem:- ∫ x8 ex^9 dx

Q: Evaluate the integral by making the given substitution. dx u = 7x + 8 (7x + 8) '

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Q: Consider the indefinite integral dr: (a2 + 1)

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Q: 3, 1

A: ∫0∞x3(x2+1)(x+1)2dx put   x3 = u=> dx = 3 x23du => ∫0∞x3(x2+1)(x+1)2dx = ∫0∞3u3(u3 + 1)3(u6 +…

Q: Evaluate the integrals

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Q: 3. Which of the following integrals cannot be evaluated using a simple substitution? 1 xp- x +1 ,4 1…

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Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫e3x + 1 dx

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Q: X-1

A: Evaluate: ∫x4x-1dx

Q: 2.x D' -8 .

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: We need to integrate∫ex-8x-8dx

Q: Evaluate the integral of 2e2xdx from 0 to 1

A: Our Aim is to evaluate the integral given below:-∫012e2x dx -(i)

Q: Evaluate the integrals in ∫8 e(x+1) dx

A: ∫8ex+1 dx Put  x+1=t⇒1+0=dtdx⇒dx=dt

Q: Evaluate the integral or state that it diverges. 14 -dp- x(x+ 1) 2

A: The given integral ∫2∞14xx+1dx use partial fractions 14x(x+1)=14x-14(x+1)

Q: z · 3°dz

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Q: Use the fact that 1 +C 2e2 to either evaluate the improper integral -dr, or show that it diverges.

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Q: Evaluate the following integrals.

A: We have∫x21−9x2dx

Q: Evaluate the integral. 13r In(r) dr

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Q: S x³et*dx

A: A detailed solution is given below

Q: 3X + e

A: Given integral is,

Q: Evaluate the integral ∫e−xsinh2xdx.

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Q: Evaluate the integral, if it exists.  ∫01Sin (3 π t) dt

A: Given the integral ∫01Sin (3 π t) dt We need to evaluate the above integral.

Q: Evaluate the 2 improper integrals attached as an image.

A: Evaluate the first integral as follows.

Q: 13. x-x dx x² +x?

A: We need to evaluate the integral ∫13x-x-3x2+x-2dx ................ (1)

Q: Evaluate the integrals

A: ∫1e1x(1+7 ln x)-13dx

Q: Evaluate the integral. In 5 2x 3 e X dx 0.

A: Basic integrals : →∫mneaxdx  = eaxamn Properties of Logarithm : →aln(x) = ln(x)a. →elnx=x.

Q: Evaluate the integral or state that it diverges.

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Q: Evaluate the following integral. ∫ 2z5e1-z dz

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Q: 7)In(6) dx

A: The objective of the question is evaluate the indefinite integral.

Q: [²₂ 0 y√2y - y²dy

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Q: Evaluate the integral of (e^x)^(1/2)

A: Given the integrand (e^x)^(1/2) Evaluate the given integral using u-substitution method. Let

Q: Evaluate the following integrals.

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Q: Evaluate the integral. (In(5æ))² dx +C

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Q: 7. S√4x²+9dx

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Q: + 3x dz. x2 + 1

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Q: (d) / (In m)ª dr.

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Q: Evaluate the integrals in ∫e1/x/x2 dx

A: Our Aim is to evaluate the integral given below:-I=∫e1/xx2dx -(i)

Q: Evaluate the integral.

A: Our Aim is to evaluate the integral given below:-I=∫xe2x(1+2x)2dx  -(i)

Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

Q: the integral of dzwhere e is and 9-x S

A: by using Residue theorem we can solve the given complex integral

Q: Evaluate the integral by making the given substitution.  x^5/ (x^6-7), u=x^6-7

A: