find sin x cos? x dx 75. 76. sin 2x sin (cos 2x) dx er dx et + e* (e2x + e)² dx 77. 78. x + 1 e* + 1 79. dx e*(e2x – 4) 80. x4 - x3 e* + e3x dx e2r (e* – e¯*)(e* + e¯*)³ dx 82. 81.

Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: 3x+sinx-3 tan x -) Given g(x) = ln- calculate g'(x). %3D 3x4-Vx

A: Given gx=lnx3+sinx-3tanx3x4-x We know that lnab=lna-lnb. Therefore, using this formula we can write…

Q: dp Find dx given p(x) = (sin?(3x))(3x²-4*)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f·g' The Power rule;…

Q: 11. Find e*sinx dx

A:

Q: sin(3x)e°*dx

A:

Q: Solve dx dy for y= sec (In x) In (tan x)

A:

Q: -2 e* sin(x) -dx 1+ x2

A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

Q: sin (3x+1)dx 4 cos (3x+1) C

A:

Q: 1-S 1-sinx dx 1-sin?x -sin²x

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

Q: sec (x) tan (x) dx S S cos(x) sin (x) dx - log2 (x) dx

A: Important points: 1. If the derivative of a function is present then assume the function as t and…

Q: (a) y = In(sec²x) (b) y ecos + cos(e) x² −1+2 (c) y = x (d) y = sin² (e) y = (f) y = (cos(√sin(x)))…

A: Let's consider  the properties of differentiation.Let f(x) and g(x) are two different function…

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: The complex form of integral can be converted to simple integral using integration by substitution…

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: x? + 4x + 1 dx (x - 1)(x + 1)(x + 3)

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. L 16x dx 2. o &. + 2 +1 3. (sec x- tan x dx dx 4. cos x tan x 1/4

A:

Q: sin3 x dx (③)글 4 () (0)

A:

Q: 1 Evaluate – -dx 1+ 3sin"x + 8cos™x

A:

Q: at (x = })? dy Csc(3x) Sin(3x) + Cos(x), Find Let y =

A: The given function is: y=csc(3x)sin(3x)+cos(x)  =csc2(3x)+cos(x) To find the derivative of it:…