5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

Q: 3x4-4 cos x = -6

A: Find d2y/dx2 implicitly in terms of x and y3xy − 4 cos x = −6

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: (a) [ dx ? 元+1

A:

Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

A:

Q: 7) x sec (x)dx

A: We will solve the problem

Q: Q4// Find the value of csc(sec-1 2) + cos(tan=²(-V3)).

A: Here  given as Use some trigonometric formula as

Q: eXtan(e*) dx sec²(e*) – 7 2(, - 7

A:

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: 6. sec (sin-1 x)

A: Interconversion

Q: Use the variation of parameters to solve the following equation: d^2y/dx^2- 3 (dy/dx)+2y=cos⁡(e^-x)

A: I am attaching image so that you understand each and every step.

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: 2 sec2( sec-1x)dx xVx² -1 3. 3.

A: Here  we evaluate    ∫32 sec2sec-1xxx2-1  dx

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

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Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

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Q: x* + 4 dx : %3D 3

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: What is tan-¹(2x²+1)³? dx 1 (2x² +1) +1 3(2x² + 1)² (2x² +1) +1 12x(2x² + 1)² (2x²+1)6+1 x²(2x² +…

A:

Q: (Sin ² x - y) dx - tanx dy =o

A:

Q: 7) | sec x. dx

A: Given:       ∫ sec5x dx

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 6メ-8) - $(4)= =1 Cos x (8-x9- 15) %3D

A: Since in part 1st given equation has no rational roots so I will do 2nd question

Q: t 3X +5) C

A: on doing integration we get

Q: 5 一=A+hxsl-x dy=?

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Q: / (cos(x) + Ex dx 4 +

A:

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below

Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

A:

Q: tan² (x) sec¹(x) dx.

A: Given, ∫tan2(x)sec4(x)dx

Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

A: