Q1.2 Part 1: Integral Q1.1 Response: ICGvernment of Western Australia South Metropoistan TAFE Response: S[4x5 + 3x-2-5x-¹ + 2]dx √ [(x²+6x+5) +3cos(x-4)]dx UEENEEE

Q: 2 х3 +3х6 1 x4

A: Explanation of the solution is given below...

Q: 17x-6 - dx x² -x² - 6x 2.

A:

Q: (x² - 12x + 9) dx (x²-3x + 2)²

A:

Q: S. 2 x 2 x +9 -dx

A:

Q: 6+02+z*91taXtrực (x + 2)(x² + 3)² xp=

A: ∫3x4+4x3+16x2+20x+9x+2x2+32dx

Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

A:

Q: 9x +1 d) / | 3 – g² + 9x – 9) x2 + 9x – 9) -

A:

Q: 5x2-12 х-12 dx х3-4х

A: Given: ∫5x2-2x-12x3-4x

Q: S(4x3 + 9x² + 4x – 1)dx -

A:

Q: х3 (2 — х?)1?dx x3 dx 1 — 2х2 1 x²dx Vx2 + 4

A: ∫un du = un+1n+1+C ∫a2+x2 dx = xx2+a22+a22sin h-1x2+C ∫1x2+a2 dx = sin h-1xa+C

Q: So dx VL-4X2

A:

Q: 2x3 – 9x2 + 11 dx x2 – 4x + 1

A: We know, ∫dxx=lnx ∫xndx=xn+1n+1 for any real number n.

Q: 85 MATH2215 2x+1 dx x2-7x +12 2x+1 メー4XX-3) B. (X-4) (X-3) ACX-3)+ B(X-4) てメー4)CX-3) = Ax-3A+Bx-HB…

A:

Q: 1 e2x + 5ех 4 e2x + 4ex

A: Given: ∫ 14e2x+5exe2x+4ex dx= 14∫ ex+20ex+4 dx    (Multiply and divided by e-x)

Q: x-1 2 x² + x -dx

A: As per the question we are given an indefinite integral of (x-1)/(x2 + x) which we have to evaluate.

Q: x-4 -dx x² – 5x +6

A:

Q: 1 x2 - x + 12 x3 + 3x dx

A:

Q: - Trig Sub x5 dx (36x2 + 1)ž

A:

Q: S 1 (x + ²)² + ( √ 39 ) ² 2 dx

A:

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: a) + )- (2x2 - 3x) = x² + x- 2x – 3x = (x² – 2x) + (x- 3x) = -x² - 2x

A:

Q: (1 1x +15x* – 17x³ – 6x² + 7x – 4)dx -3

A:

Q: 7x - 4 3 – – 4x 4x² dx

A:

Q: Vx +4 dx х Vx-4

A: Consider the integral ∫x+4x−4dx Therefore, ∫x+4x−4dx=∫xx−4dx+∫4x−4dx...…..(1) Let I1=∫xx−4dx and…

Q: (5- 4x2 dx 3 + 2X 4,

A: We can find the integral as below.

Q: f(2x. (2x + 6)5 dx 0 (2x+6)6+ C 2 H|M 3 12 (2x + 6)6 + C (2x + 6)6 + C (2x + 6)6 + C

A: A detailed solution is given below.

Q: Evaluate 2x-4 (x-3)(x-1)(x+3) -dx

A:

Q: Show that E(x-a) = E(x; -x) + n(x- a), squares about a = is smallest. other words, show that the sum…

A: The answer is as follows :

Q: (5Vx² – 4 4 3) dx 2,

A: Given data:     The given integral is: .   The given integral can be written as, Here, I1 is the…

Q: d. 2x³ + 1 x4 + 2x 12x -dx h. 1 ²x² - 2x + 1 x² dx

A: