5 +2.x3. 2 Evaluate the integral f+2 dx. 4 x* +x

Q: Q.1 Find the integral of f 2 /x+ e* ) dx. - 3

A: We will find the integral as following.

Q: I. Evaluate the following integrals. Зx3—2х2-4х-3 dx x² (x²+x+1) 2.

A: Given: I=∫3x3-2x2-4x-3x2x2+x+1dx   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: - 23 L f(2)dx = 11 - 82 and - 23 L g(z)dæ = 30 82 and – 23 h(x)dx = 25 - 82 | what does the…

A: Given ∫-82-23Fxdx=1 -1          ∫-82-23gxdx=30-2          ∫-82-23hxdx=25-3We find…

Q: 8. Evaluate the integral. 2 2 (a) S(4x°. 3x + 2x)dx - 1 4 4+6u (b) S(ou)du Vu 1

A: Using rules of integration & formulae of integration.

Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: Evaluate the integral / (x" + e*) dr

A:

Q: 9. dx Evaluate the integral| - 3 x( In x) 3 9. dx 3 x( In x) 3 II

A:

Q: 5x (x² +a) dx is In +eTan-1X The resulting integral of + C, where a, b, d, and e are integers. What…

A:

Q: dr

A: Given integration is : ∫x2-9x3dx To find the value of integration.

Q: 3x -dx x4 + 1 Evaluate the indefinite integral. + C

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Q: Consider the functions given.Evaluate the integrals

A: given: ∫16f(x)dx=10∫16g(x)dx=5∫46f(x)dx=5∫14g(x)dx=2 to evaluate ∫468g(x)dx

Q: (a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2…

A:

Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: definite 10) Evaluate the s Integral S dy 1x+7

A: We need to evaluate the following integral ∫04dx1x+7

Q: Q2) Evaluate the integral x dx a -0.

A:

Q: 2x3 + x2 + 4x+ 29 dx. Evaluate the integral: (x² – 2x + 1)(x² + 2x + 9) -

A:

Q: -1 2x Evaluate the integral dx = 0 x*+1

A:

Q: 6.3.28. Evaluate the integral. using U substitution integrate (x^2)sqrt(x^2-1)dx

A: Use substitution method, to evaluate the integral

Q: Question-10 Evaluate the following integrals. a) S ( + 10) dx +e 3x

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: dx (§5.7, Q28) Evaluate the indefinite integral: (x – 9)5"

A: step 2 complete solution

Q: 6. Evaluate the integrals So (x² +1) e-* dx a- b- Sx2V2 + x dx

A: Given :(a) ∫01(x2+1)e-xdx(b) ∫x22+xdx

Q: -Arctan + dx The integral of the given function S (x²+4)2 is Arctan + C 8(x²+4) 16 b. - Arctan- + а.…

A: Given:   ∫dxx2+42

Q: Зx2 — 4х — 9 A + х — 2 Evaluate the integral J x³ – 2x² – 9x + 18 dx using + х — 3 x + 3

A:

Q: (2x2-3x+2) dx (x-1)2 (x-2) - Evaluate the following integral: S

A: To evaluate the integral: ∫(2x2-3x+2)(x-1)2(x-2)dx

Q: -5e 1 Evaluate the integral: dx. 1 x A. - - 1 5e B. 1+ In 5 C. 0 D.00

A: We have to evaluate to integrate

Q: Evaluate the integral. dx (х — 13)(х — 23) (Use symbolic notation and fractions where needed. Use C…

A: Explained below

Q: 8x dx Evaluate the given integral: S; 4x2-5

A: Here we have to evaluate I=∫8x4x2-5dx

Q: 5. Evaluate the improper integral S₁ 1 (x-3) 5/3 dx.

A:

Q: 8) Evaluate the indefinite Integral S x ³ √√₁₁ + x ²4 dx

A:

Q: Q2) Evaluate the integral x3 dx 3 a *0.

A:

Q: a) [₁ 3]: Evaluate the integral 3x - 1 (x + 4)(2x - 1) / dx.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 3x3-7x+1 dx # 2) Evaluate the integral X-2

A: As you have asked to solve #2) we will solve only #2).The given integral:∫3x3-7x2+1x-2dxWe will…

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: ー2X 2 e Evaluate the integral 4え |

A:

Q: 9) Evaluate the following indefinite integrals a. [(5x¹ + x² + x) dx b. 9x²(x³ +5)*dx c. S7 C. dx…

A:

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: 1. Evaluate the integral: x/x – 1 dx.

A: answer = 1.0667   explanation is given in below step

Q: Evaluate the integral / (x² +z=3) dr.

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Q: 7. Evaluate the definite integral by hand. x dx -1 x' +1

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Q: Q/ Find the integral 1 + X dx 1-X

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Q: Evaluate the integral. (x6 + 4y³) dy -3

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Q: 5. Find the indefinite integral of the following functions : Hint: use integration by parts (a) / -…

A:

Q: 5x |(x²+ a) The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers. What…

A:

Q: II. Evaluate the following integrals: x- 2 1. J- -dx +1 2. J; -dx 8х + 3 3. J- x -4x-9

A:

Q: 3 Evaluate the integral: J3 a(x-3) dx Answer:

A:

Q: 7 Suppose f(x)dx = - 3, f(x)dx = - 6, and g(x)dx = 3. Evaluate the following integrals. 2 2 2 g(x)dx…

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Q: 2. S (x+1)dx x²(x-1)

A: We can find the answer in the following steps.

Q: dx Evaluate the improper integral (x-3)2

A: Given query is to find the value of the integral

Q: Q1\ Evaluate the integrals: 10 A. S- V16+x2 В. Г(3 — 2х)-5 dx

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.