2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan 0 (x-2)=s sec O

Q: Find sec42x -dx tan 2x A --—-—-cot²2x-—-—-cot³21+ C 16 cot82x) (4sec22x-1) B -(cort2x) 4 12 11 1 C)…

A:

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: Determine 3 sec(9x) tan (9x) dx

A: We have to determine the value of integral: ∫3 sec 9x tan 9x dx Solving given indefinite integral by…

Q: x – sin 2x -dx x + cos2x

A:

Q: 15. (D* – 1)y : = sin 2x

A:

Q: sin 3x dx 3-10cos3x 10.

A:

Q: 1 √₁-² 1- Evaluate -dx (1 - 3x)²

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: sec(2) tan(2) – 1 dz 3.

A:

Q: Calculate Sin(5x)=-√(2)/2

A:

Q: (1-sin9x)²dx

A: To evaluate the given integral

Q: ~|J O 1- Cos 2πTX) dx L x (1. 2

A:

Q: sec² (x) tan° (x)dx

A:

Q: tanx sec² x.dx COS X √√2+ sin x dx

A:

Q: y = Secx ( sinx+ Cosx)

A: Given, y=secxsinx+cosx And we have to find the dydx.

Q: 4(cos- (-3x)) = dx

A: Given query is to find the derivative of cos-1(-3x).