3 ( tann cax) sech' cax) dx Iet v = +anh Cax) = 2 sech cax) dx dx = du 2 sech' cax ) u sech ca* ) du 2 sech' cax ) du %3D +anh' cax) 3 + C +anh'c sc3)) II

Q: Find the intergration of x^3(x^4-sine)^5 dx

A:

Q: Integrate: S sin3x cos²x dx

A: The given integral is ∫sin3xcos2xdx

Q: 5. Integrate: [tan(7x)dx

A: 5) The given integral is ∫tan7xdx

Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

A:

Q: sec?x Integral tanx

A:

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

A:

Q: Integrate: S tan (æ) sec³(x)dx

A:

Q: Section 3.4-The product rule and Quốtiént rule In(x) Differentiate: Y dy Preview %3D dx

A: Given: y=ln(x)x9

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

A:

Q: find integral tan 5 x sec 7 x dx

A:

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

A:

Q: Evaluate f, f,(1-2) L(-dy dx dz

A:

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: Integrate (three) of th 1) f sin6x cos3x dx

A:

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

A:

Q: tanx 4) S Edx Cosxv1+secr 5) S(1- u)vudu

A:

Q: sin(6y) sin(8y) dy.

A: Topic - integration

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: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: sec Vn du in

A:

Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

A:

Q: If Z= sinh () x- show that:

A:

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: d Use quotient rule to prove [cscx] = -cscxcotx. dx

A:

Q: 3- - 플 플 sin²cyl y จน

A:

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

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

Q: Integrate by Gaussian quadrature (n=3). dx Ji 1+x*

A:

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

A:

Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

A:

Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: х2 9 dy + sinx - у %3D0 dx

A:

Q: integrate 1/(sin^2(3x) dx

A:

Q: 11 tanto-2 tan Bz1 show that 2 coste- Cos B20

A:

Q: Integrate (tanx)^3(secx)^3

A:

Q: (7 – siny)y' = 3x2 + 2x

A:

Q: sin 2x dx 4. J2osin cosmetin2xdx

A:

Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

A:

Q: 13) Estimate tan(44°) using linear approximation.

A: