13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3 In lxCx?ょs) 3. +27X c) In olin13x (x²+G)+9tan-?ax7C 3tan 3 In x)+ 2x In lx?+91-3 tam -ス 3/C

Q: sing the relation z=x+iy = rcosθ + irsinθ=re^iθ . Derive z^n = r^n(cosθ + isinθ)^n = r^n(cosnθ +…

A: The relation .The aim is to derive the expression .

Q: fx/0=x) REAL Vay (y + 2x=y-x)

A: We have to identify the correct options.

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: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

A:

Q: 2dy Зу-4

A:

Q: Rind the Domain Jx-3 x2 16

A: Given query is to find the attached domain of the expression.

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

A:

Q: (2) DE (D² D²-70³-11 0²-80-12/9=0

A: A detailed solution is given below.

Q: Bolve * LOB3X + 3inxt é Ars: 1 = De B o83X -3_8in2 18 3x m , 18

A:

Q: (ах + bx? + сх + d dx . (ax' 2 Eхample 34.

A:

Q: Use substitution to evaluate the integral | (3x³ + 5)° . 27x²dx

A:

Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: solve differtial eauatiun 6x dy +(61ny+5) ¿x =o

A:

Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

A:

Q: Prove or disprove: 3n = ω(2^n ).

A:

Q: Integrate: - da 9x2+16 O In (3x + v9x2 +16) + C O In (3x + V9x2 +16) +C ㅇ tan ' (뚜) + C 0 tan1 (부) +…

A: Given ∫dx9x2+16

Q: Đi bỏ xes xdx = dx 2) √ √9+4x² = a) 6e5-1 25 ¹ (²3) + a) cosh-1 c b) 1+4e5 25 b) (4e5-1) 25 c). sinh…

A: Using following formulas

Q: Prove that a b π √√(x − a) (b − x)dx : = (b-a)² 8

A: To prove that,  ∫abx-ab-x dx=π8b-a2

Q: 2 4 | 6x V1+4x dx

A:

Q: 64+ 203 - 6D² - 16D -8)y =D

A:

Q: Why the minimal polynomial x^2 - (sqrt(2)+sqrt(-2)) splits into linear factors over K?

A: Assume K is a field that includes the square roots of both 2 and -2. The formula for the element  α=…

Q: 1) x'+ 64 - 0 2) x* - 7x + 12 - 0

A: We have to factorize the given expressions. 1. x3+642. x4-7x2+12=0

Q: Evaluate ∫ ∫σ x^2 + y^2dS, where σ is the portion of z =√3(x2 + y^2) for 0 ≤ z ≤ 3. Exact answer is…

A:

Q: 3. Prove the Distributive Laws: PV (q^r) = (pVq) ^ (pVr) and p^(qVr) = (p^q) v (p^r).

A:

Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: 1 4[Vx(ax* + bx +c ]= 2Nx -(5ах* + 3bx + с) b)

A: We have to find  the derivative for the given function

Q: ~3 Evaluate 6x* + 2) dx. -3

A:

Q: The possible values of Re (i ^1/2) + | Im (i^1/2) | a) −1,1 b) 0, 2 c) 0,1 d) 1, 2

A:

Q: Eliminate the arbitrary constant in the equation: a.) x²y = 4+Cy b.) y-x = C1e^x + C2e^-2x c.) y =…

A: