find sin x cos? x dx 75. 76. sin 2x sin (cos 2x) dx er dx et + e* (e2x + e)² dx 77. 78. x + 1 e* + 1 79. dx e*(e2x – 4) 80. x4 - x3 e* + e3x dx e2r (e* – e¯*)(e* + e¯*)³ dx 82. 81.

Q: 10. [x'sin(x')dx 11. [x sin(x)dx 12. [sin(x*)dx 13. ſe* dx 14. [xe* dx 15. [cos (x)dx

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Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

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Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: s sin² (3x) cos³ (3x) dx Hint: cos²x = 1 - sin² x 07 sin²x = 1 - cos² x

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Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

Q: Find the derivative and show your complete solution of the following 1. cos(e ^ (2x) + e ^ (- 2x))…

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Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: This problem requires integration by parts. Find ∫(xsinx)dx sin x - x cos x   - x cos x   cos x - x…

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Q: sinx+5* dy for y=In dx e3Xtan(x³) O a. Some other answer cosx+5*In5 3x²sec²(x³) - 3 tan(x³) b. dy dx…

A: We have given y=ln(sinx+5xe3xtan(x3)). Let us simplify right hand side using logarithmic…

Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: 9. 2x+4 4 1+ (x + 2)² 1+ (x + 2)² (b) Using suitable method find [2 tan¹(x+2) dx. (a) Find - dx and…

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Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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

A: In some cases indefinite integrals can be converted to standard integrals using an appropriate…

Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: Q-6: Evaluate the integral 1). dx So Jie-1

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Q: integral of cos x sin^3 2 x dx

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Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: 4 cos (4x)(-4 sin (4x))dx. Evaluate the integral 4 cos (4x)(- 4 sin (4x))dx%3D

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Q: 3- Find dy/dx for y = log2(1- sin (3x2) %3D

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Q: (x² +1)Z. tan-1(sin 2x) Q2/ B/Find dy if у 3 dx (x2 +4)3 . sin-32x

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: e-V2x sinh x sin x x dx

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Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: 211 3- sin nx dx [1-cos2nx]dx 1t, where n %3D

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Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

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: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

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Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: 8) S(eax - e-ax) dx 9) S; sinh x dx 1+cosh x

A: Answer to question number 8 and 9 are as below,

Q: Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

A: Given                   y43= sinx cosx1+2.lnx

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 4 cos °x sin x dx 3x sin: 1/3

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Q: 7. Integral cos x dx sin x

A: This question is related to integration, we will solve it using given information.

Q: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: 3e° 3ecsch 3x 11) -dx sinh 3x tanh 3x

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Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

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: Cos x dx In x (sin x) () - dæ. (In x)²

A: We have to find the value of the integral : ∫cos(x)ln(x)dx-∫sin(x)1xln(x)2dx

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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