11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx' . cosax dx 2x - sin ax + cos ax- a 2 - sin ax + c) (ans. : a a 14) f sin(Inx) dx (ans. : (sin(In x)-cos(In x )) + c) 15) fIn(a' +x' )dx (ans.: x. In(a' +x')- 2x+ 2a tan +c) a

Q: Find formulas for the following general indefinite integrals to verify results (7), (8), and (10) in…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Use a change of variables or Table toevaluate the following definite integrals.

A:

Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

A:

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A:

Q: Use a change of variables or Table toevaluate the following definite integrals.

A:

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

A:

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A:

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Given:  Calculation:  Let ln(p) = u Differentiate both sides (1/p)dp = du Also the limit of…

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A:

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: s nip

A: Given z=tanα2

Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: In(cos ax) ? limx-0 In(cos bx)

A:

Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: Consider the following integral: ∫0π8cos2xdx Use the following formula to solve above integral:…

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

A:

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given: ∫x6-3x24x5-xdx

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: Use Table to evaluate the following definite integrals.

A: Given: ∫0110xdx

Q: 1)f sin 4xdx cse(2+3lnx) dx 2) fcos 2xdx 7)f sec (4x)dx 3) fx tan(2x2 +1)dx 8)fx csc| 3- dx 3 dx…

A:

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: ∫ex3+2exdx Put, 3+2ex=t⇒0+2ex=dtdx⇒2ex dx=dt⇒ex dx=dt2 Therefore,…

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: To evaluate: ∫0π2sin2θ cosθ dθ Solution: Let substitute t=sinθ dtdθ=cosθdt=cosθ dθ Limit will also…

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given integral is:

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Definition used -                 U substitution -                     ∫f(g(x))g'(x)dx =∫f(u)du ,…

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

A:

Q: Use Table to evaluate the following definite integrals.

A: The given integral is ∫0π40cos20xdx   formula used: ∫cosaxdx=1asinax+C

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: The given integral is ∫04p9+p2dp. Let x2=9+p2. This gives  2x dx=2p dpxdx=pdp. when p =0,  x=3. when…

Q: 1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

A: To prove:-

Q: 1- у-In (x' +4) -x tan' -1 х 2 y = e2x²-3;

A: We will solve the following

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

A:

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A:

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

A:

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: To evaluate the integral: ∫ew36+e2wdw Solution: Let substitute t=ex Differentiating both sides, we…

Q: when

A:

Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

A:

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Given     ∫(x+1)42xdx Formula ddx(xn )=nxn-1 ∫xndx=xn+1n+1+C

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: the given integral is: ∫04xx2+1dx we have to use a change of variables or table to evaluate the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.