Q3/ By using definition, proof that cot x = dx csc2 x.

Q: 5- (tanx + secx)2 dx

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Q: Calcula te Y Sin X dX ,n=Lo by SimPSon rule

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Q: السؤال 3 -Sec2 (). dx tan (5). · dz O ). de tan tan . da O ). dz O tan

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Q: 1- tanhx = sech x

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

Q: ( sinh3x cosh³x dx

A: Consider the integration as I=∫sinh3xcosh3xdx

Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: tane cote +- = sin0 + cose %3D 9. Sece csce

A:

Q: Evaluate 1 dx 1-sin x

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Q: L[sin bd]- show that

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Q: Find [sinh-(cotx)] and simplify completely. d dx

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Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

Q: differntiate y= (lnx)^(cosx)^(sinx)

A:

Q: इसे १५ Sin 2X *3 tant 2X Lind ds_2

A: Given that the function is   y = 2sin2 2x × 3tan-1 2x To find the dydx

Q: S tan (2x)sec (2x)dx = %3D

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Q: Find y' if cosh x sinh?

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Q: ntegrate using trigonometric substitution: dx 25+x2

A: It is in the standard formula  form of integration

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

Q: Evaluate x sin (5x)dx x sin (5x)dx=

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

Q: Ssin | sin" x cos" x dx if find

A: Odd function :- When the function is of the form f(-x)=-f(x) i.e., when the value remain same but…

Q: Solve the equation for x  arcsin√2x = arccos√x

A: The given equation is sin-12x=cos-1x

Q: What is the definition oi sec(x)?

A: We have to elaborate definition of sec(x )

Q: #4 tan lun sec x dx 4.

A:

Q: Integrate cot(x) In(sin(x))dr.

A: The answer is found in step-2

Q: coth*(sin 3z) 12) zp- V1- ? 3z tanh

A: Integration of given function

Q: Evaluate the integral.

A: Given: ∫01 tan-1x1+x2 dx To find: Value of the integral.

Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: S 4 sec(x) tan(x) dx

A: We will use standard formula here

Q: (3X dx =? Sinmply

A:

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

A:

Q: Use Trigonometric Substitution to evaluate |x'V1-x° dx

A: put x= sin t for trigonometric substitution.

Q: Differentiate with respect to x. Y=sin5x

A:

Q: use a geometry formula to find the exact value of the definite interval square root of 16-x2 dx on…

A: The given can be consider as a function,

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: coth“ (sin 3z) -dz /1– tanh² 3z 12)

A:

Q: /x[cosh?(2x²) – sinh²(2x²) ]dx is equal to

A: solution :let…

Q: 1. ſ tan5 2x sec3 2x dx

A: Let,I=∫tan52xsec32xdxI=∫sin52xcos52x1cos32xdxI=∫sin52xcos82xdxI=∫sin42xcos82xsin(2x)dxusing…

Q: (cosh ' []] 1s dz

A:

Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: ㅠ St tan5 (2x) sec² (2x) dx

A: Given:∫π2πtan5(2x)sec2(2x)dxsubstitute u=tan(2x)differentiate on both sideswe know that…

Q: (tan 2x + cot 2x)² dx x2 + 2x dx 3+ 3x² +1

A:

Q: /is [sec2(x) – csc²(x)]dx Evaluate:

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Q: (cotx + tanx)² dx 3 4

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Q: Jam sin(10x) dx

A:

Q: Se-Ax .sinh(2x) dx

A: We know, sinh(x)=ex-e-x2

Q: Use variation of parameters to solve csc(t) y = et. sec(t).

A: Given: Let us consider the given y=12-121y+csctsectet and solve by using a variation of parameters.

Q: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…

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Q: Evaluate the indefinite intergral ∫sin(-10x) dx =

A: This question can be solved using integration by substitution.

Q: Sec tan (5x) dx

A: