secx-1 sin x %3D V secx+1 1+cos x

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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)…

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Q: sinx dx cos³x (1 – sec*x)3 A)를 (1-sectx)-4 +C B)를 In(1 sec*x)3 + C c)금 (1-sec+x)-2 + C D)름…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: sin(-4x) cos 3x dx 1. 3

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Q: h(x)= sin¯' 3x– 6x sec x² -1

A: The given function is  h(x)=sin-13x-6xsec-1x2

Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

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: (i) * cos x + cos x tan²x dx sec?x (ii) |x – 2| dx (iii) | x²/x* + 1dx

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Q: 3) (sinx + cos x)² = sin 2x + 1 COS %3D

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

Q: sec x-1 sin x %3D secx+1 1+cos x

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Q: 4x 3x + cos (2x² + 1) tan? x) x (1+ sin² dx

A: Here We have to evaluate;  a) ∫4x3x+cos(2x2+1)dx b) ∫tan2x(1+sin2x)cos2xdx

Q: S [tan® x sec6 x + cos“ x sin“ x + sin* x] dx

A: Given that: (tan8xsec6x + cos6xsin4x+sin4x) we solve this integration by using general formulas of…