Question 6 (: The indefinite integral 2+1 dx equals (a) [1/x²] In(x2 + 1) (b) [1/x]In(x² + 1) () [1/2]In(x² – 1) (d) [1/3]In(x² + 1) (e) [1/2]In(x² + 1) a A e

Q: - 9 √²x²=2 dx = √² ((x² + 1) = 10) dx 1 + 10 1 +

A: ∫01x2−91+x2dx=∫01((x2+1)−101+x2)dx

Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

Q: Which of the following is 1ln x dx? (a) 1/x + C (b) x . ln x - x + C (c) 1/2 . (ln x)2 + C

A: Evaluate ∫1lnx dx. Apply by parts law of integration: ∫fg dx=f∫g-∫f'∫g Let f=ln x and g=1 ∫1lnx…

Q: What is the y-intercept of y= csc x

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Q: Compute 1 (x² + 1)(x² + 4) Lo -dx.

A: Given ∫-∞∞1( x2 + 1 )( x2 + 4 )dx

Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: Evaluate the definite integral. (Be sure to show your work.) (a) / (2³ + 1)dx (sin x + 1)dx 2 (b) /…

A: Since you have posted question with multi-parts. As per guidelines, we"ll solve only first three…

Q: QUESTION 2 a) Evaluate the integral | dx (x-5) +5 b) Show that 5+4x - x² = 9-(x-2) by completing the…

A: (a). From the given problem: I=∫5x-52+5dx   ...1 Let, u=x-5So,ddxu=ddxx-5dudx=1-0du=dx

Q: 1. Basic Integration a. fx(x + 1)dx b. S √ √x+x² dx x C. √₁²|x-1|dx

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Q: Can you please answer this question

A: Ans (a):Ans(b):Ans(c):Ans(d):Ans (e) page 1:Ans (e) page 2:

Q: Y= xy3x=5 (унуза

A: This is question of calculus  Here one equation is given  We have to decompose  it by apply both…

Q: if f(x) = 15 - g(x) for [-2,2], then what is the integral of (f(x)-g(x))

A: To find the integral of f(x)−g(x) over the interval [−2,2], we first need to express f(x)−g(x).…

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: (b) Let 2.4 (r) = 5z+9 (*- 1)(z+ 1) Evaluate the indefinite integral S(r)dr. Hint: Do long division…

A: b) Given :   Let fx=2x4-5x+9x-1x+1               ∫fxdx=∫2x4-5x+9x-1x+1dx        Performing…

Q: 4x + 4 -dx. Choose all of the following that are correct. x² + 1 Consider the definite integral

A: To evaluate: ∫014x+4x2+1 dx Solution: We know that, ∫f'xfxdx=lnfx+C ∫1x2+a2dx=1atan-1xa+C

Q: Find the indefinite integral (x² + 2x)e**+3x² dx ©^ ( = x² + x²) +²+3x² +C Bex³+3x²+C c. 1 D. e 13…

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Q: integrate the following

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Q: the integral of (15tan-1(x))/x2

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Q: Use the reduction formula: [(In 2)" dx = 2(In x)" — n f (In 2)¹-1, times. First application of the…

A: Given: ∫(ln x)n dx=x(ln x)n-n ∫(ln x)n-1 dx     ........(1) By using the above result we have to…

Q: -2x xp- (1-x)' 7. Evaluate A. +6x-n(1-x)+-(1-x)* +C C. '+6x + n(1-x)' + (1-x)*+c D. x+6x + In(1-x)"…

A: