a) 1 – tan e² xp- 5) //2+9x²dr c) (x² – 6x + 10)² dr |z' In zdr x' In V64 - a -dr e)

Q: 2)( L[ (1 – 27)' sin 2r.dr)) =

A: Using the formula

Q: Question 2 Integrate: 16x 10 dx 4x2- 5x + 81

A: Given,         ∫16x-104x2-5x+81dx

Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: da Evaluate x² V4

A:

Q: 3) Integrate √√√x-csc² 4 + sec(3x) tan(3x))dx

A:

Q: (3Vr + 2e) dx.

A:

Q: 3) v = C,e2x cos 3x + Ce sin 3x 2x

A:

Q: dx Evaluate x²/4 x²

A:

Q: 1 -dx cos.x-1 2) Integrate

A:

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: e' [ S (5² +a²) 2 ] = t sinat 2a 7 Prove using Convolution

A:

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

A:

Q: Integrate f cos(x) dx

A:

Q: Question 4 Calculate the given integral: / tan (4x) dx 1 1 a) 능 -tan(4x) + 4x + C tan’(4x) + 12 1 b)…

A: We have to solve the integral

Q: ∞ sin2x dx (x²+1)²

A:

Q: 16) Prove the 1+ tan?(u) = sec2(u).

A:

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: Differentiate. y= In [(x+7)* x + 8)®(x +2)°] dx

A: Given y = ln(x+7)4(x+8)6(x+2)3

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: Question 7 Calculate the integral: /x' cos (2.x²) dx 1 o- sin(2x³) + r cos(2r*) + C b) O sin(2r*)…

A:

Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

A:

Q: Q2) A Differentiate the following ( 1)y= [(5x) (4- 2x)]²

A: As per bartleby guidelines we only give first question answers.

Q: Cos 56 CUST J sin'sB-sinsB dB

A: Consider the provided integral, ∫cos5βsin25β-sin5βdβ Find the expression for the provided integral.…

Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: Use the addition formulas for sinhx and coshx to prove that tanh(u+v)= tanhu+tanhv/ 1+tanhutanhv

A:

Q: 故(x3+5) ex A al d Iny d in5x

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: a) Compute the quotient (22 + 2i) / (2 + 2i) b) Suppose z = (In 2) + i (pi/2). Compute e^z

A: " Since you have posted two questions, we will solve first question for you. To get another question…