Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

Q: Evaluate the integral. (Use C for the constant of integration.) | 16 In(V) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 3 dx x(x4 + 5)

A: In this integrated we will assume x4 =t , then we will solve it

Q: Evaluate the integral. (Use C for the constant of integration.) x5 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

A: Given ∫8xx+c5dx

Q: Evaluate the integral. (Use C for the constant of integration.) (x2 + 2x) cos(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dt 1- t10

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Q: Evaluate the integral. (Use C for the constant of integration.) (x2 - 9x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

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Q: Evaluate the integral. (Use C for the constant of integration.) x² + 9x + 1 dx (x² + 1)2

A: Make two parts of the integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 10x2 cos(mx) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 6 dx 2x + xVx

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Q: Evaluate the integral. (Use C for the constant of integration.) 7x2 + x + 7 dx (x² + 1)2

A: The given integral is: ∫7x2+x+7x2+12dx To evaluate the given integral.

Q: Find the integral xn ln x dx; n ≠ −1, n real. (Use C for the constant of integration.)

A: we have to use integration by parts ∫uvd=u∫vd-∫du∫vdd  and ∫xndx=xn+1n+1+c where c is the…

Q: Evaluate the integral. (Use C for the constant of integration.) /1+√x ox dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 dx J x(x* + 3)

A: ∫1au+bdu =1alnau+b+C dxndx=nxn-1

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 7x + 1 dx (x2 + 1)2

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Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

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Q: Find the Integral. (Use C for the constant of Integration.) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 9x cos(8x) dx

A: Integrate this by integration by parts

Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x + 20x + 104

A: Consider the provided integral, ∫x+21x2+20x+104dx Evaluate the provided integral. Apply the…

Q: Evaluate the integral. (Use C for the constant of integration.) x²e&x3 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: Evaluate the integral –4x3/2 In(x) dx, x >0 Note: Use an upper-case "C" for the constant of…

A: Evaluate the integral

Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Evaluate the integral. (Use C for the constant of integration.) х dx x2 + x + 3

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Q: Evaluate the integral. (Use C for the constant of integration.) X + 14 dx + 2x + 5

A: Topic - integration

Q: Evaluate the integral. (Use C for the constant of integration.) 21 dx 3x + xVx + x/x

A: Explained below

Q: Evaluate the integral. (Use C for the constant of integration.) 7 dx x(x* + 1)

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x cos(6x) dx

A: Let, u=x and dv=cos(6x)

Q: Evaluate the integral. (Use C for the constant of integration.) sin (x) cos (x) dx 4.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: Evaluate the integral. (Use C for the constant of integration.) (x2 + 3x) cos(x) dx

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Q: Calculate the integral. (Use C for the constant of integration.) dx XV 36x4 – 1

A: Given, ∫dxx36x4-1 We have to evaluate the integral.

Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) dx x2…

A: Given: ∫dxx24x2+81

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: Evaluate the integral. (Use C for the constant of integration.) -2t te dt

A: Let the given function is:

Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx Vx + xVx

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

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Q: Evaluate the integral. (Use C for the constant of integration.) x-5 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) Vx dx

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Q: Evaluate the integral. ( Use C for the constant of integration. )

A: The given integral is ∫x+21x2+20x+104dx. Evaluate as follows.

Q: Evaluate the integral. (Use C for the constant of integration.) 16 In xp (x^ +C

A: Topic:- integration

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx xV 9x2 - 1

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx XV 5 + (In(x))²

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Q: Evaluate the integral 8(x – 9) J (x + 5)(x – 2) ** Note: Use an upper-case "C" for the constant of…

A: Solve by substitution and simplify.

Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx 4 + (In(x))?

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Q: Evaluate the integral. (Use C for the constant of integration.) | VER-X² dx 81 x

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Q: Evaluate the integral. (Use C for the constant of integration.) | (x – 3)sin(xx) dx

A: The given integral:∫x-3sinπxdxWe need to evaluate the above integral.We will use integral by parts…