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Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

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Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

Q: Evaluate the integral. sec (5x + 8) tan (5x + 8) dx

A: ∫ sec5x+8tan5x+8dx

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: Evaluate 7`-3z²+4x-8 dr dx 프(22+4) O In#(2? + 4)*| + In (2 + 4)* + -글tan 1 (플) + C Omp(22+4)| + -tan…

A: The solution is given below in the next step:

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: Evaluate the indefinite integral. 5dx x In(8x)

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A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

Q: evaluate the indefinite integral.

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Q: Evaluate the integral. 24. '8 -2/3 dx

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Q: Evaluate. 2tan2120° +2sin2150° -cos20° 5sin2300° +csc2150° -sec230°

A: To Evaluate. 2tan2120° +2sin2150° -cos20° 5sin2300° +csc2150° -sec230°

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A: Consider the given integral. I=∫sec9θtan7θdθ Further, simplify.…

Q: tnes) メ edx. Uince) LnC2)

A: Given: I=∫ln2ln5exdx we know that ∫exdx=ex+c

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Q: use method of false position. to Selution acccurate to- within lo -3x°=0 for osxsI and 3€x<

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A: Given query is find the value of the integral.

Q: (8) If fCx) = 3x*- +4X +1, Sind

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A: Given : (sin ax)(cos bx)

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Q: Evaluate: / sec (5x + 1).5dx Select one: O cor(5x+1) + c O tan(5x + 1) + c O cor(5x) + c O tan(5x) +…

A: Use the substitution method and simplify the given integration than integrate.

Q: prove tan^4x=cos4x-4cos2x+3/cos4x+4cos2x+3

A: Basic trigonometry proof

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A: Recall: ∫1xdx=ln(x)+C

Q: 271/3 2. CSC 58. 1/3

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Q: Show that dx = x² – 8x In (7 + 4/3). -

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Q: Evaluate /5 sec(8 x)dx In(tan(8 x)+sec(8 x)|) + c 8. 5 In(|tan(8 x)+sec(8 x)|) + c 8. 05 In(|tan(8…

A: By using proper substitution and formula integral can be easily solved.

Q: integrate sin"ueg ceasu) where n=824

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Q: sec 2x CSC 2%

A: Solution: Consider the given integral: Now, rewrite the integral: Let u = cos 2x

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A: Given expression: cosx+cos2x

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Q: Evaluate the integral. 5) 5.7x 5 dx 9 - 4 A) -- In|9 - 7x |+ C B) -5 In|-9 + 7x | + c 5 C) In|-9 +…

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

Q: sec(2 In x) tan(2 In x)

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Q: Evaluate the definite integral 10z2 + 4 dz 5 108 5 16 2

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