5. Find : 60 y= (b) y = cos (11x³ + 5x). dx

Q: Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

A:

Q: dy Q10., Solve (1+ x²) + y = tan¬1x. dx

A:

Q: Find y' and y". y = cos?x

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Q: 6. dx dy + cos.

A: Given: dydx=yx+cosy-xx

Q: Find ∫√(2x − 1) dx.

A: Given:

Q: COS V4- x2 dx -2 1/2

A:

Q: If y = cos¹ (v₁²), X = find dz? 1 Vu² +1 2= ln (2x-3y)

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Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: • / VI - x² dx

A:

Q: Differentiate y = In (cos² 3x).

A:

Q: Find dy/dx. Do not simplify the answer. 4* +4 csc a.) y = log4 x-csc(4) b.) x3 y + cosh¬1 3 = e –…

A:

Q: a cos(x²)esin(z²) da -ут 10. TT

A: To find the integral.

Q: •T/2 cos“ x dx. OS

A:

Q: Se-¹x² dx. е

A: Given query is to find the integral.

Q: (b) ( cosx) = -sinx dx

A: To Determine: find the derivative of cosx Given: we have a function cosx Explanation: we have a…

Q: y= sin (0.25) + sinh (2).

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Q: 3.a) Find dx y = ln(2x - 4√x). b) Find dx y = ln(In(sinx))

A:

Q: Solve: y (cosx)= (9+ y²)

A:

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: Solve (cosx)dy = (sinx)dx

A: The objective is to solve the expression cosxdy=sinxdx

Q: Y= 5-e- COSX by %3D

A: Given: y=5-e6y=cosx( This question is don't have to specify word  find  and how to find the answer)

Q: (1 +Iпx) dx x3

A: The given integral is ∫1+ln xx3dx. Here, u=1+ln x  and  v=1x3.

Q: sin() cos( 2

A: To Find :   ∫sinx2cos3x2dx   Note: 2sinAcosB=sin(A+B)+sin(A-B)

Q: Evaluate Set 7x cos (6x) dx. Sex cos (6x) dx =

A:

Q: 2a xsin " dx 1.

A:

Q: dx = 3 cos° x/2sinx

A:

Q: y = cos(-4x)

A: