(a) r+1+tanh² (E) d.x r2

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: Q5) Find fs) if you know that g(x) cos(x- 1). fx) = 3tan(x) at r2

A:

Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

A:

Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: Ex/show that y = eax sinh bx satisfies y" - 2a y' + (a² + b²)y = 2 b2 e ax sinh bx

A:

Q: find general Solution (D²+6D. Sin 4X to

A: Given differential equation is : D2+6D+16y=sin4x To find the general solution.

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

A:

Q: Find f(x).

A: Given,

Q: dx -= In[F(x)]+C. What is F(/3) For (x+x³) (x Tan-lx+ 1) 3. B.

A: We have to choose the correct option according to the given information

Q: 5. w = x tan-y - 2=

A: Given: w=xtan-1y-2xyz

Q: Solve the initial value problem : f'(x) = cosx + sec²x, f (÷) = 2 +÷. %3D

A: Solve the differential equation by separation of variable and use given initial value to eliminate…

Q: For x >0, tanh(Inx)+ dx x2 - (tan-(x)) 1 + > = x? .2 Select one: O True O False

A:

Q: y= (1+x?)tan x- x? y' = 1 + xtan1-2x y' = 1 + xtan -2x y' = 1 + 2xtan 1-2x y' 1 + 2xtan -2x y'…

A: In this question we are required to calculate the derivative of the function.

Q: find the given limits

A: we have to find the limit limt→-1t3i+sinπ2tj+(ln(t+2)k

Q: tanr sec r dx 3

A: Here we will find the antidarive.

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A:

Q: If y = tanh"(k/x) and x (1 - 144x) y'=A Then A= .

A: First we find the derivative of the given function y.  After that we substitute k=12 in the result…

Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

A:

Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

A:

Q: 1 tan 2 1 1 + tan-x +C. 2 2

A:

Q: a) f(x) = 1+ Sinx for all x e R

A: According to the question, we need to plot the graph of the function: f(x) = 1+sin x The graph of…

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A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

Q: 3. Derive the reductive formula for f sec" (x) dx.

A:

Q: (B) The evaluation of f- -dx is (x*+3x2 +1)[tan-( In|tan"+5| + e -In tan-( +c (i) (ii) (iii) None of…

A: No antiderivative could be found within the given time limit, or all supported integration methods…

Q: "/2 sin x dx Jn/a V1-2 cos x 4.

A: As per the guidelines  we can answer only one question at a time. If you want to get the answers  of…

Q: dx -= In[F(x)]+C• What is F(/3) if C = 0? For J (x+x³) (x Tan-'x+1) + 6 + -1 +

A:

Q: Q.No.3 Evaluate Sx cosec-xdx.

A: Explanation of the solution is given below....

Q: L sinh-t %3D .a 3s2-4 6. .b O 9s2 -4 .c O s2-4 3. .d O 2s2-4

A: We know that  L( sinh(a)t) = (a)/(s^2 - a^2)

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A: Question 1,Given,          sinh3x=3sinhx+4sinh3x

Q: dx -= In[F(x)]+C. What is F(/3) if C= 0? For (x+x³) (x Tan-!x+1) (A

A: We will integrate first then find F(x).

Q: Q3) Solve for (y) if: In(y-2)= In(sinx)-x .... Q4) find for : y= sin(x") + 2* + n

A:

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

A:

Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-'x+1) -1 + - 6 -1 + - + -15 -is -İS

A: Given: ∫dxx+x3xtan-1x+1=lnFx+C                              …1 We have to find F3 when C=0

Q: .2. COS X sın.x.ços.Xdx

A:

Q: Q2: Evaluate: * Jx* sin(1- x)dx?

A: use substitution method to solve the integral

Q: dx -In[F(x)]+ C. What is F( 3) if c = 0? For (x+x³)(x Tan-!x + 1)

A:

Q: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: Ex/show that y = eax sinh bx satisfies y"- 2a y' + ( a² + b²)y = 2 b² e ax sinh bx

A:

Q: Solve the initial value problem : f'(x) = cosx + sec2x, f(÷) = 2+. %3D

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

Q: Solve the equation for x, where x is restricted to the given interval. y = 3 tan (2x - 1), for x in…

A:

Q: lifferen tiake 3-Co5hx with respect to X 6+ sisht

A:

Q: dx - = In[F(x)]+C•What is f(/3) For if C = 0? (x+x³) (x Tan-!x+ 1)

A: A detailed solution is given below

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: dx For (x+x³) (x Tan-'+1) =»[F(x)]+C. What is F(/3) if C = 0?

A:

Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

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A:

Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: 211 If f(x) = sinh(- In c) then f'(r) 27

A: Given,        fx=sinh-lnx

Q: x² (d) S √1-4x² (HINT: sin² t = dx. (1. (1 - cos 2t).)

A: We have to evaluate ∫x21-4x2 dx.