Integrate the given function. T/ 20 2 sec 5x -dp- 4 + tan5x 1/20 2 sec 5x 1 5 -In 4 - 4 + tan5x | LO

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

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Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0

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Q: 2x-1 Q:If y =f| and f'(x) = sin x, find x* +1 dx

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Q: Solve the given ODE using the method of variation of parameters y" + 4y = sec 2x

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Q: 6. (2x + 3y)dx + -x)dy 0 %3D

A: Consider the given equation as 2x+3ydx+y-xdy=0

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

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Q: 193. у - 2 sin z 1/2

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Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: Find the period of the function y = sin(2x + 1.5). %3D 2 2 2л

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Q: dy Solve x da + 5y = x sin (ax2)

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Q: Solve the following by Substitution Method. (show complete solutions) a.) y(x tanx + ln y)dx + tanx…

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Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

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Q: b) f(x) = tan (VInx) %3D

A: f(x)=tan^-1(sqrt(lnx))

Q: 10. f sin x dx 25+cos²x

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Q: 5) f(t) = f(t) = e¯2t/1+ sin2t

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Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

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Q: Integrate the given function. 234 sec 3x dp- 9 + tan3x T/ 12 2. sec ²3x „1/ 12 1 10 dx%-xin 9 9 +…

A: We will evaluate  the required integral.

Q: Differentiate the following: a)y = 2e3x b) f (x) = In(3x² +x + 4) c) y = tan-(2x) d) y = sin-(5x)

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find if y = tan- 5). Select one: A. 1-) В. 1+ (1 – 2)* C.d - 2 O D. I+ (1 - 1)* OE.+ (1-)

A: Given function is We know that derivative of tan inverse x is 1/1+x^2,so

Q: f(t) = 2t2 - 5 sin(3t) %3D L{f(t)}

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Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: tan x- 2x°y = c 3

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Q: Evaluate: +3) V1-x2 19. dx A. V1- x² + arcsin x + C C. - V1- x² +3arc cos x + C B. – V1- x² +3…

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

Q: 5. (D² + 25) y = sin x + cos 2x

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Q: Integrate the function. dx x2+ 8x + 32 A (2x + 8}In]x2+ 8x + 32|+ C B X+4 tan + C 4 sin + C (*+4)…

A: First simplify then use the formula of integration and get the final result

Q: dx Select one: a. sec-(x2) + C b. 2 sec-(x) + C c. -sec-(x) + C d. 1 sec-1(x²) + C

A: We will use the substitution, x² = sec (theta)   Then we will proceed as follows :

Q: (2 tan¯'n – T)

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Q: function hlx) = x4+Sx23 at given values and simelify Evaloate the of the nde Pendent variable…

A: see below the calculation substituting the values of the independent variable in the place of x

Q: If f(x) = tan-(2x), then f'(x) = %3D %3D 1+4x? (B) 72 (C) 1+4z² (D) 교 1-4x (E) 2(sec-'(2x))²

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Q: 4. f(t) = (e^(10t)) sin(2t) 5. f(t) = (e^(9t)) sinh(5t)

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Q: d (i) Show that (2 dx -1 X 3x x tan 3 = tan-1* 3 x2+9 V3 i) Hence evaluate (tan dx . 3

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Q: Exercises: A. Find for the following: dx 1.y = (5x+3)6 2. y = sec(2x) + tan(2x) 3. y = In(x²-3x - 1)

A: To find the derivative of given functions.

Q: Integrate the function. x² - 25 dx x² - 25 2 - O A. sec +C 25 Vx² - 25 О В. 5 -1 sin + C 5 OC. 5 In…

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Q: Evaluate /43dx (x-3)²+3 2 국.cot-l V3 + C (=) +c x-3 tan-! O None () +c -3 . tan-1

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Q: 3 sin³x sec?x dx = Select one: а. b. 1 С. d. 1 1/3 1/4

A: Topic:- definite integration

Q: Evaluate dx 4x4+4x2+17 2x 8 sec-1 2+1 + C O None of the choices. Please refer to my solution. O…

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Q: 프-3r-dx= a) 클m3x + 21+ tanx + C b)습 미3x + 21-tan'x + C Q13:J +1)(3r+2) d)흘 I미3x + 21+ tanx + C -1…

A: The integration of the integral is  (2x2-3x) /[(x2+1)(3x+2)].

Q: y = Ax tan(X), an dy 3T+3 %3D Find A. 6. 5 7 4.

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Q: 5. Compute f sec (x) tan(x) dx

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Q: Evaluate: X + T/4 dx. -*/4 2- cos 2x

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Q: 1 x³ -1 y =e*(dsin 3x- tanx')+- 10 y' = ? (fx +1)

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Q: Evaluate sin 2t dt. t 8.

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Q: V5x d (7?). tan dt dx

A: Use the concept of derivative of an integration then simplify.

Q: dy 1. Find 2 for the given function by differentiating it implicitly. dx ac tan-1 1- o

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Q: tan3x y = sec 2x

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Q: S 7 tan (2x) dx 2 Hint: tan²x = sec ² x - 1

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Q: JV t kan (4x-) tan (4x-1) Sec (4x-1)

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Q: Find F'(x). SOLUTION IN HANDWRITTEN|| 1 1. F(x) = √²2dt -2x-³ 2. F(x) = ²x²²x cos x² dx

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