Evaluate the integral using integration by parts where possible. x In(8x)dx

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 36 +…

A:

Q: Evaluate the integral using integration by parts where possible. (x + 1)e* dx

A: ∫01x+1exdx = ∫01(xex + ex)dx = ∫01xexdx + ∫01exdx ∫ex = ex + c Therefore, ∫01exdx = e -1

Q: Evaluate the integral by integration by parts: TT √3 x² cos x dx

A: To evaluate the given integral by using integration by parts.∫0π2 x2 cos x dx

Q: Use integration by parts to evaluate the following integral: Sx sinx dx

A:

Q: Q2: Evaluate the integral ° In xdx using by parts formula

A: We use integral by part

Q: ( (x? + 1)e* dx

A: Given

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A:

Q: Evaluate the integral using integration by parts where possible. r In(8r)dx

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Q: e√x √xdx

A: To evaluate the given integral

Q: Evaluate the integral. (Use C for the constant of integration.) 5x+e5z te* dx

A: Given,            ∫6e5x + e5x dx

Q: Evaluate the integrals

A:

Q: 1. Sx tan?x dx

A: topic - integration by parts

Q: Using iterated integrals, find the area bounded by x2 − 6x + y = 0 and x2 − 2x − y = 0.

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

A: To evaluate the below integral Simplify it

Q: Evaluate the following integrals using integration by parts xF ex dx

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Evaluate the following Integral using integration by parts X CSC X S - dx CSCrCOU

A: Use by parts method of integration

Q: 28. e cos 2x dx ,3x

A:

Q: Evaluate the integral using the Integration by Parts formula with u = In(x), dv = x° dx. (Use…

A: use integration by parts take

Q: 32x12 In(x)dx

A: since u have asked multiple questions in single request so we will be answering only first question

Q: 2. J cos x In (sin x)dx

A:

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

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Q: 2. S cos-1 x dx

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Q: dx 2

A:

Q: ydy (y–1)*

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Q: Evaluate the integral using appropriate substitution: (ii) x^2√(1 + x)dx

A: Let the given integral be y - y = ∫x21+x dx         ..................(1)Let,u2 = 1+x…

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of | (x2 -…

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Q: x Inx dx

A:

Q: Find or evaluate the integral using substitution first, then using integration by parts. cos(In x)…

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Q: Evaluate the integral using integration by parts. 9x° e 2x dx 2x dx =

A: Given, ∫9x3e2xdx

Q: | x²ln(x) dx 1

A:

Q: 3. Evaluate the integral using integration by parts: |p° ln p dp

A:

Q: evaluate the integral using the Integration by Parts formula with the given choice of u and dv.

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) ( 16 +…

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

A:

Q: Evaluate the integrals ∫cot3 x dx

A: We have to evaluate the integral: ∫cot3 x dx Rewriting the integral, ∫cot2 x cot x dx We know the…

Q: In x - dx

A: Given integral,           ∫eelnxx2dx

Q: Evaluate the integral using tabular integration by parts. (2 x² – x +3) e +C -

A: We can evaluate the given integral by the tabular integration by parts method.

Q: Evaluate the integral using trig substitution: ∫x2√(3+2x-x2) dx

A: The integral function is ∫x23+2x-x2dx

Q: Evaluate the integrals ∫1/x√ln x dx

A: Given ∫1/x√ln x dx . We need to evaluate the integral.

Q: Evaluate the integral using Integration by Parts. | 5x2 cos 2x dx COS

A:

Q: Evaluate the following integral using integration by parts. x¹ ln x dx

A: This question is based on integration by parts.

Q: Evaluate the integral using Integration by Parts. x-e* dx Use C for the arbitrary constant. x²e* dx…

A: Topic:- application of integration

Q: Evaluate the integral using integration by parts. 4x dx Xe 4x dx = Xe

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Q: 64. y cos(x³ – 1) dx dy y/2

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Q: Evaluate the integral by interpreting it in terms of areas.  integral 0 to 10    (|x-5|) dx

A: Given  The integration is I=∫010x-5dx

Q: Evaluate the integral using appropriate substitution ∫(x^2 +1)/(√(x^3 +3x))dx

A: Given an integral: ∫x2+1x3+3xdx Let, x3+3x=t t=x3+3xdt=3x2+3dxdt=3x2+1dxdt3=x2+1dx Substitute value…

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 4 +…

A: Given

Q: Evaluate the integrals ∫2 cot πx dx

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

A:

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

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.