T/2, 1) S7[tan³x + tan³x]e=tan²x %3D 1/2

Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…

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Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand?…

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Q: 18) e2x = sin(x + 3y)

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Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

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Q: S sin (2x – 1)cos (2x-1)dx (2х - 1)dx

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Q: Compute d/dx  sin-1 (x/x+1)

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Q: The solution of sin'x + 2sinx - 3 = 0 on 0°Sx< 180° is:

A: ⇒sin2x+2sinx-3=0⇒sin2x+3sinx-sinx-3=0⇒sinx(sinx+3)-1(sinx+3)=0⇒(sinx-1)(sinx+3)=0⇒sinx-1=0  OR…

Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: on of period 2 pi in t. (x+sin r)(x

A: The differential equation is given as, dxdt=x+sin2tx-esint Let x=ft be the solution of the…

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: 11. Integrate. a. x3 b. S(5 tan 3x – 2 sec2 x)dx

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Q: dy Cos(3x) + (In x)

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Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

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Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: The value of x2 in the given equation of f(x) = x3 + cos(x) would be equal to initial value of -1…

A: The given problem is to find the value of x2 for the given function with given initial values Given…

Q: 8. y = In(2e-t sin t)

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Q: Ssin (2x)cos(2r)dx

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Q: S2ta J 2tan x In (cos x) dx=

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Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: S sin(3x + 2) cos(1 – 4x)dx

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Q: 1) S ur [sin(In x)+cos(ln x)]² dx

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Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

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Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

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Q: (e²)(sin²2x) Compute In y and In 5z

A: Basic log formula are applied to solve the question.

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: too ·00 dx COSX x² +hx+5 =le Residue solution cos (2)

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Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: 1. x In x dx 2. x'e-3* dx 3. tan- x dx sin Vx 4. dx

A: Since you have asked multiple questions solving first 3 questions. Please repost other problems.

Q: 4 sin' 2x cos 4x dx 4.

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Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

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Q: Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

A: Given                   y43= sinx cosx1+2.lnx

Q: . Find the solution 2 SP dt 5t³S³ Determine the general solution of dx =1+ 3y tanx.

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Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: 3) e4x = sin(3x + 4y)

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Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: 5.S Vsin 2x . cos2 x dx

A: Integration is a process of adding up infinitesimally small pieces of an area. There are mainly 2…

Q: 9. [sin Ssin' cos–dx 3 3

A: (9) To evaluate ∫sin5x3cosx3dx Substitute sinx3=u and cosx3dx=3du. Therefore,…