x² + 2x- 10 (2 dx = x² (x² + 4x + 5) (2x + 4) + 1) (2x+ 4) +1) x2 + 4x + 5 x2 2 Consider dx - evaluate dx - x2 x² + 4x+5) 2 - In(x2 + 4x +5) - Arctan(x + 2) + C 2lnx 2 – In(x² + 4x + 5) + Arctan(x + 2)+C 2lnx + 2 2lnx – In(x² + 4x + 5) + Arctan(x+ 2) + C - 2 - In(x2 + 4x + 5) - Arctan(x + 2) +C 2lnx +

Q: 1) Use the Substitution Method to find f 12x (3x² + 4) dx . O 20(3x^2+4)^10 +C O 0.2(3x^2+4)^10 +C…

A: The given integral is 12x(3x2+4)9.

Q: Integrate (2sinx+3cosx)2

A: Integrate (2sinx+3cosx)2

Q: Differentiate and simplify: y= (3 – 4x)²* O a.y' = - 2(3 – 4x)²*-4x + (3 – 4x)In(3 – 4x)] Ob.y'= 2(3…

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Q: How would I solve this problem using the product rule?

A:

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: -メ~1) (メ-2) (x+3)? xp (1-X-

A:

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

A:

Q: Show that In (x+ Vx? + 1) x2 x + Vx2 + 1 dx x + / 2v x² + 1 X + V x2 + v2 +1 + 1 Vx+ 1 x2 + 1

A: This is a derivative problem

Q: 12) x+(6x + 5)___dx √√x6 + x³ + 5 S

A:

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

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: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

A:

Q: 5 S(4x² – 12x +9) ²dx

A: We use here binomial expansion and then we  integration.

Q: intergral ((x2 -3)/(x4 +7))

A: Solution Given ((x2 -3)/(x4 +7)) we need to  find the integral

Q: 3-J (х* + 2х 3) dх

A:

Q: (10x-19) (3r + 2) (5x-3)

A: We will use the exterior angle property of a triangle that states that an exterior angle is equal to…

Q: express     n-1 Σ((k^2)/n) k=1   in closed form.

A: The given question is related with closed form of finite sum. Given that,…

Q: Calculate (3+1 x3+x a) using partial fractions b) using the substitution w = x3 +x

A: a) Given : ∫3x2+1x3+xdx  By Partial fraction  First, factor the denominator, we get 3x2+1xx2+1 =…

Q: How many total solutions can the following funnction have? F(x)=3x^8+6x^4-2x^2+5x-4

A:

Q: csc/x+5 xp- 1) Use substitution method to evaluate Vx+5

A: Given:         ∫csc2x+5x+5dx     apply u-substitution     u=x+5→dudx=12x+5       dx=2x+5du…

Q: /x + 3 + 4 – x > - 3

A: Answer

Q: x³ + x 10) √ (x²+ + 2x² + 5) dx

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Q: 3-2 7) 6 – z*

A:

Q: ·25x +8x +43x" (3x4-11x² +9x²-11x+6) (9x²+12x+16) Find f Ax+B C(3x+2)+D 9x²+12x+16 + x²+1 dx if this…

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Q: Find the coefficent of x^6 in the following: (1 + 2x + 4x^2 + 8x^3 + ...)(3x^2 + 3x^4 + 3x^6 +…

A:

Q: S 2x(ex²+1 – 2x*) dx

A:

Q: Evaluate x²(x³ +9)¹/² dx 2 +9)³/2 +C Nia O (x² +9) ³/2 +C O C(x² +9)³/2 O x³ +9+C

A:

Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5[x]/ is: 5x^2+ 5x +1 4x+1 O x^2+2 None

A:

Q: 3/4(8y-9)<3

A: We multiply both sides by 4 first.

Q: Find the general antiderivative. f(3 sin x-3cos.x) dx Select One 3cosx + 3sinx + c -3cosx - 3sinx +…

A: We have to find antiderivative.We have to find solution.

Q: 5x 3x2 (3x²)' ework Diffeventiate the equntion. /3

A:

Q: Evaluate: [(5x* - 2х* + 3х - 4)dx

A: Evaluating the integral