Consider using the method of partial fractions to solve dx x²+x+1 2x²+2+x³+x - dx = [Aƒ (x) − B ln(g(x))] + D ſb da, and if A = ‚B<0, then g(x) = x+2 x² +1 In(x²) In(x²+1) x + 2

Q: If f(x) is even and 5 [₁(f(x) - f(x) 8) dx = 8, find -5 5 [²³F(x) f(x) dx.

A: ∫-55fx-8dx=8 ∫-55fxdx-∫-558dx=8 ∫-55fxdx-8∫-55dx=8 As, ∫dx=x ∫-55fxdx-85--5=8 ∫-55fxdx-8×10=8…

Q: If E (X) = 1 and Var (X) = 4 then E (X² + 2X – 1) = :- 1)

A:

Q: If h ( x ) = 3 x 2 − 2 x, then find h (5).

A: Let there is a function fx to find the value fa we need to substitute x=a in the expression.…

Q: Find the extrema of f (x) = 2x3 − 15x2 + 24x + 7 on [0, 6].

A:

Q: Finally, use the Generalized Power Rule to determine[x -x], noting that x-x is the difference of two…

A: Here we have to find differentiation of f(x)

Q: If f (x) = x + 1, and g(x) = 2x, then f (g(x)) = [ ? ]x +[ ] %3D Enter

A:

Q: 2 Find [f(x) + 5g(x)]dx if 2 |f(x)dx = 8 and / g(x)dx = -1. -4 [f(x) + 5g(x)]dx = i -4

A:

Q: and g( x) = 7 − ( x − 3)^2 , a.) Solve for x: f ( x) = g( x) (Answers c

A: Inequality: a)f(x)=3x3-4x-3g(x)=7-(x-3)2f(x)=g(x)3x3-4x-3=7-(x-3)23x3+x2-10x-1=0The solution isx≈…

Q: Find (x) + 6g(x)]dx if f(x)dx = 9 and / g(x)dx = -3. 3 F(x) + 6g(x)]dx = i

A: Solution...

Q: 1. Find for y = In () (A)+ 1 3x-2 X-1 1 x-1-x2 (B) x2 - -- x-1 x (х-1) x2 x2(x-1) x-1 1 X-2 (D) (E )…

A:

Q: Find the domain of v. v (x) = x + ln(7x - 4)

A: Find the domain of v. v (x) = x + ln(7x - 4)

Q: f (x) = (8 − x)(x + 1)2

A: It is given that     f(x)=(8−x)(x+1)2 We have to find the zeros .

Q: dx x1/2 + x2/3 6 ln (x1/3) + 3(x1/3 - 2x1/6) +C 6 ln (1 + x¹/6) + 3(x1/3 - 2x1/6) + C Evaluate (A) B…

A: The given integral is                                      ∫dxx12+x23

Q: Given g(x) = In(7x+x), the derivative g (x) is

A: Given,           gx=ln7x2+x

Q: Let g(x)=x2+6x        and f(x)=4x       Find each of the following.      a)  g(−1)      b)…

A:

Q: Determine the formula for the the function f below. p(x) 1 1 - 1 12 1 3 72 1 4 432 2.

A: when x=1 p(x)=12=3·16 when x=2 p(x)=112=3136=3162 when x=3 p(x)=172=31216=3163 when x=4…

Q: Give the formula for f(n) (x) where f(x)= 1/(3x-1)

A:

Q: Find f (x). f(x) = 2 In (1 + 7x?) f(x) = %3D

A: f(x)=2ln(1+x2 ) Differentiating w.r.t x both sides, we have f'(x)=2ddx (ln(1+x2))…

Q: | [10f(x) – g(x)]dx if Find 5 5 f(x)dx = 7 and g(x)dx = 6. %3D | [10f(x) – g(x)]dx = i

A:

Q: 14 Find [3f(x) – g(x)]dx if 14 14 | f(x)dx = 3 and g(x)dx = 9.

A: Topic = Integration

Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

A:

Q: A company manufacturing skateboards has fixed costs of $60 per day at and total costs of $500 at a…

A:

Q: - 2r³+ 4x²+ 3 -dx is equivalent to x²(x²+ 1) 2x- + - 1 dx x?+1) 2x –1 dx x²+2, 3 B © /: 2x – 1 x+1…

A: Given problem:-

Q: · [2² 1. ² dx

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: ind a formula for f-¹(a) and (f-¹)(a) if f(x)=√ =-¹(x) = f-¹)'(x) =

A: Given query is to find the inverse and the derivative of inverse.

Q: (a) (b) 12 in (1 + √5) In 3 In 2 (c) (24) (d) - In (1+√3) =)/In (1+ √5) √ √2+1 dx = ? In 2+√3

A: The given integral is

Q: y=In [e 7* (x° + 5) (x³ + 8x)] d [In [e 7* (x³ + 5) (x° + 8x) ]] = ] dx

A:

Q: Determine the real root of f(x)=x4-8x3-35x2+450x -1001. Using false-position method to locate the…

A: