d Verify tanh - = X 1- x2 dx

Q: Find the indefinite integral.

A: We have to solve the indefinite integral: ∫tan x3 sec2 x dx Solving the integral by substitution…

Q: EX / Show that cosh x-sinhx=1

A:

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

A: 5) The given integral is ∫tan7xdx

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Express in exact form: In(x² + 1)dx

A:

Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

A:

Q: sech (x*) tanhl 12.

A: 12. Given integral is ∫sech3(x13) tan h(x13) x23dx Let us make substitution to simplify the above…

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: Evaluate the indefinite integral: ∫ sec2 x tan4 x dx

A: Evaluate the indefinite integral. ∫sec2xtan4xdx Let tanx=tsec2xdx=dt

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Find integral.

A: We have to find the integral: ∫tan 7x dx We know the integration formula, ∫tan x dx=lnsec x+C∫tan ax…

Q: Find the indefinite integral ∫sec6 4x tan 4x dx

A:

Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

Q: Find the indefinite integral ∫ (6 sec x tan x − 5 sec2 x) dx.

A: Given:  Let I=∫6 sec x tan x-5 sec2 xdx To Find: To evaluate the given integral.

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

A:

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: Find the indefinite integral ∫tan5 x sec4 x dx

A: Given:∫tan5(x) sec4(x)dx

Q: Find the indefinite integral. ∫ sinhx / (1 + sinh2x) dx

A:

Q: 1 dx Ji x/1- (In x)²

A: ln x = tdxx = dtx=1 → t = ln 1, t=0x=e → t = ln e, t=1   I = ∫01   11-t2  dtFormula:∫ 1a2-x2  dx =1a…

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: 3 dx V16-x²

A:

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: Ve 1 dx x/1 /1- (In x)² 1

A: To find the integration.

Q: solve \int (sin^(5)x)/(cos^(2)x)dx

A: We evaluate  \int (sin^(5)x)/(cos^(2)x)dx

Q: Evaluate integral x^2e^-x^3 dx

A:

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

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

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

A:

Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: tanh 2x In (cosh 2x)dx

A:

Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: calculate the integral.

A:

Q: Find the indefinite integral

A: Consider the integral: I=∫sec42x5dx……1

Q: cosh(In x) dx

A:

Q: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: Find the indefinite integral. sec 3x tan 3x dx

A: Given integral, ∫sec53x tan3x dx

Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Find integral 2  to 5    1/ sqrt  (x -2 ) dx

A:

Q: find integral tan 6 x sec  4 x dx

A:

Q: 8. Scoth 2x In (sinh 2x) dx

A:

Q: Use differentials to approximate tan (43°). Round to 4 decimals.

A: Approximate to tan(43°) using the differentials ,