x'(3+ x) (x + 4) 49. (x + 5) (x – 1) noiu -

Q: integral: 5x sec2 (x) dx

A: ∫ 5 x sec2xdx

Q: 7. h(x) = tanx- tan 8. h(x) = 3 sec-x

A: we have been given the equations to differentiate w.r.t x

Q: 5). § sech x tanh-x dx

A:

Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

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Q: 3.sin (2 4. (4 sin 3x - x) dx

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Q: 6. Solve (cotx - 1)(2cosx + 1) = 0 where 0° sxs 360°. Show your work. %3D

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Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: 1) lim y-4 x+6x+5 2) lim 2-3x-4 t+3t2-12t+4 sin3h-2h 3) lim 4) lim 3-4 gin

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Q: 2 tanh(x) 2) tanh(2x) (H.W) 1+ tanh (x) 2

A:

Q: solve using reduction of order (D^2+1)y=tanx

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Q: 2 tanx + 7tanx+ 5 sec2x 2 tanx + 5 X. %3D

A:

Q: / (6x" – 7Va+ 19x- 8 -- + Evaluate + 14e0* + V11 dx. (You don't have to show the work.)

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Q: tion of all components of v(3) correct to two decimal places.

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Q: 35) y=x.tanh (ans.: x. tanh x(Vx sech' x +2 tanh x))

A:

Q: Verify the identity.

A: Given: arctanx=12arctan2x1-x2. The interval given is -1<x<1. From the given interval, let…

Q: Solve cot x-v3 =0 over [0,2t)

A:

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

A:

Q: | sin x (3cosx)dx 2: VZ 3x dx V1- x4 3:

A: SOLUTION-

Q: cosh x sinh x dx 2 (cosh x + 3)

A:

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

A:

Q: 2In|tanh(0.5x)| + C 4tan-le0.5x + C E 21n|csc(0.5x) + cot(0.5x)| + C

A:

Q: How is integration by substitution related to the Chain Rule?

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us…

Q: sinh(3-j5) (3 + j4)4 13-j7 (3 – j5)(2-j7)

A: Given sinh(3-j5)3+j443-j52-j73-j7.  To evaluate the given expression.  The formula for…

Q: S(sec x tan x – 9x³)dx =. - - sec x – x+c O sec r + x° +c O tan x + x +c sec x + x° + c sec 2 — 29 +…

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Q: 3. y = (- at x= 3 x+1

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Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: sc 2x - cot 2x = 0 1 sec²x

A: We can find the answer as below.

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

A:

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

A:

Q: e-V2x sinh x sin x x dx

A:

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: cIn3 Sn tanh(x) sech³ (x) dx In2

A: This definite integral is based on the Substitution method.  The detailed solution is explained in…

Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

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Q: 3 sinº x dx 4 Show that

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Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: 9. S sec³ x tan x dx

A: Given ∫sec3xtanxdx We know that  ∫secx.tanx=secx + c ∫xndx=xn+1n+1+c

Q: sinh-1x = In (x + vx² + 1) %3D

A:

Q: Numerically integrate f (x) = x° +3x + 4x – 6 from a = 1 and b = 2 using Single-Trapezoidal Rule…

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Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

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Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: Q/Evaluate Integral:- sec2 3x dx tan23x-3 tan3x+2

A: To evaluate the integral:

Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

A:

Q: sec² x 12. S 1+tanx

A: here we use       ddxtanx=sec2x see below the calculation and answer s

Q: 3. SIX f- - dx x in x√√(inx)2-9

A:

Q: etan x dx 1 – sin²x

A:

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step