m-1 1 + m 1 m m+2 ¹tan (+2)(x) + —tan" (x) + C m-1 1 + m 1 m+3 Ɔ+ (*) (1 - 1)² + (x) (1 + m) U²1- +(X)(₁) ²(X) (1 + r) ²²2- 1+ w 3+ (x)(1+)² + (x) (€ + ua) U²3 Evaluate > Stan" (x) secªx dx

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

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Q: 10. Given: f(x) 3= d) tan(A – B) and g(x)=x² +8 x- 5 Find: a) (f-g)(x) (g •(8))(x) i) (g-f)(3) b)…

A: Given that f(x)=1x-5 and g(x)=x2+8   (a) f-gx f-gx=fx-gx               =1x-5-x2+8…

Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

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Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

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Q: f" (x)= x(x-1)²(x + 2)³ g" (x) = x(x - 1)²(x + 2)³ + 1 h" (x) = x(x − 1)²(x + 2)³ - 1 The…

A: For any function R(x), At its inflection point, R''(x) = 0 Therefore, at the inflection points of…

Q: 2) y¨+y=1+x+x'

A: To find the general solution of  y''+y=1+x+x²

Q: [sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x); [cos(2x) – 1]+ +C + 12 8 4 sin(3x)cos(3x)…

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Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: 6. Show that when ) < |z - 1| < 2, e - ( - 3) (2 - 1)(2 – 3) Complex Analysis n=0 (z-1)" 2+2 2(z-1)

A: We use Laurent series to prove given example.

Q: sin(α+β)=()()+(-4/9)(-3/8)

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Q: f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1 – x)(1+ x) (x² + 1)² f'(x) %3D %3D x2 + 1 (a) Find…

A: Here, we are going to solve the first two subparts and for the remaining subpart please post the…

Q: 2 1.f(3x²+5) cos 2xdx 0

A: We need to perform integral. NOTE - As per Bartleby guidelines we can solve one question from…

Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

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Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

Q: Find the intervals in which f(x) =- is increasing or decreasing. log x

A: the given function is: we have to find the intervals in which the given function is increasing or…

Q: dx - = In[F(x)]+C•What is F(3) if C= 0? For (1+*;_u®L x)(g*+ x)

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Q: Performing iterations on (25) respectively, leads to the following: n-1 X2km+j v; II n-1 Y2km+j…

A: Given: 2km+j=2km+j2+rj To find: Corresponding equation

Q: Evaluate tan" (x) sec²x dx m 1 1 n (m + 2)(x) + tan -tan" (x) + C m+2 m 1 -tan (m + 1)(x) — . m+1…

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Q: Please solve for (d) as the solution (c)

A: Givena limit To find:Evaluate the limit

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: (a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

A: Topic = Derivative

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: 10. y"of y = arc tan

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Q: 5 [x²² sec (2) com ³ (2) abr dx 7 2tan can ²2 ( 1 ) [7tan² ( 1 ) +1 + C (Α 77 11 7 2x + (-) == ² (7)…

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Q: iscuss the singularities and poles of ze sinz f(z) (z-2)(z²-1)²(z²+5z+6)(z+7)(z²+4)'

A: