Find the integral of: * |x In(x + 1)dx 1 1 1 * In\x + 1| +x² +x+;In |x + 1| + € 5x² Inlx + 1|+x²-x+;In |x + 1| +c Option 4 Option 2 In |x + 1| + c x- In |x + 1|+c Option 1 Option 3 112

Q: Which of the following is equal to 64x2 - 36? 4 (4x- 3) (4x + 3) (4x +3) (4x – 3)

A: Given :          64x2-36

Q: for x belonging to Z,  prove or disprove 2x^2 +x +1 must have a remainder 1, 4, or 5 when divided by…

A: Given statement is false

Q: x + 2x + 34 (* – 10)(x^ – 25)²(,² – 8) -

A: Step:-1 Partial Fractional:- The Partial fractional is a process of taking a rational expression and…

Q: Evaluate the integral [/4x4 – 12x² +7 xdx (2x2 – 3)/4x4 – 12x² +7 – 2ln|2x2 /4x4 – 12x² + 7|} + c…

A: Given that, The integral is following, I = ∫4x4-12x2+7xdx We have to solve this integral.

Q: Determine whether x^5 + 2x^2 + 1 is reducible over Z13

A:

Q: What is the sum of (9x^2-4xy+3y^2)` and `(8x^2-y^2+2xy)`?

A:

Q: Exercise 11. Compute S 60z²(r³ – 5)°dz (11A) 2(r³ – 5)10 +C (11B) 4(r³ – 5)10 +C (11C) 240(z³ – 5)°…

A: We solve this integration with the help of substitution method.

Q: prove that 3^n is greater than n^3 for all n greater than or equal to 4

A:

Q: True or false: If a,b,m are integers with m > 0 satisfying m|(a^2 − b^2), then m |(a −b). Justify…

A: Given Information: If a,b, and m are integers satisfying m|a2-b2. To check: m |(a −b) for any…

Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

A:

Q: Find the term that contains x^8 in the expansion of (3x-1)^11

A:

Q: Find all integers x (if there exist any at all) such that x^2 + 5x + 6 is prime. Justify that your…

A: We have to find all integers x (if there exist any at all) such that x^2 + 5x + 6 is prime.

Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

A:

Q: By considering uniqueness of factorization of integers, find all pairs (x, y) ∈ N^2 such that x^2 −…

A:

Q: 1. State the equation you are trying to find a root of, which is f(x) = 0, where you define what…

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z7[x], the remainder is * O 4 O None of the choices 2.

A:

Q: dr x2 + 4x + 2

A: We will use partial fractions to solve the integral

Q: use the Pascal'striangle to expand (x+y)^(4) For f(x)=-45x^(3)-5x^(5)

A:

Q: A = [14]. -1

A: Here given A=111-1

Q: what do you get when you expand x+4/xy^2?

A: We can make it easier for you

Q: in the expansion of (x^2-(1/2x))^5 ) what is the coefficient of x^4?

A: Given that  (x2-12x)5 Apply binomial theorem:a+bn=∑i=0nnian-ibiHere,a=x2,  b=-12x ∑i=055ix25-i-12xi

Q: Show that 3x^2 + 4x + 3 ∈ Z_5[x] factors as (3x + 2)(x + 4) and (4x + 1)(2x + 3). Explain why this…

A: UFD- An integral domain in which every non-unit non-zero element can be uniquely  written as the…