6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec (11w))’ dw 8.

Q: 6. S sin x In(1 + sin x) dx

A:

Q: b) S sin 2 x cos x dx

A:

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: sin(x)ecos dx COS X 8.

A: Given,

Q: 23. x? sin (x³) cos (x³) dx

A: ∫x2sin5x3cos3x3dx=∫sin5x3cos3x3dx      x3=u,3x2dx=dx, x2dx=1/3 dx=∫sin5x3cos313dx

Q: S sin(bx) sec(bx) tan(bx) dx

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Q: Find for y = 5x sin x+ 10x cos x- 10 sin x. dx Dikdörtg

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Q: 2. 2 | sin xcos xdx

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Q: Solve dy dx + y tan x = -y³x sec²(x)

A:

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

A:

Q: [*(sin³r)√1 + cos ar dr x

A: We know that integration power rule is given as  Integration of xn is xn+1/n+1.   Here i attached…

Q: dx dx 1 sin?x +cos²x

A: given that ∫0π2 dxsin2x+14cos2x calculate the integral under the limits 0, π2

Q: xet dx (x+1)- 4.

A:

Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

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Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

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Q: | sint x cosºx dx

A: Note: We shall answer the first question only as the exact one is not specified. Please resubmit the…

Q: dx 3. S. 5sin x+12 cos x

A:

Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: S sin(1 – 2x)sin(2x + 3)dx

A:

Q: 1. x In x dx 2. x'e-3* dx 3. tan- x dx sin Vx 4. dx

A: Since you have asked multiple questions solving first 3 questions. Please repost other problems.

Q: 8. Find if y (sin x + cos x) sec x dx

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A: