dx x'V4- 8x?

Q: 2 sinx d x V1-2cosx

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Q: u+ Lut 25% 2- Sx'cosx dx

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Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: x sec2x dx (integration by Parts)

A: In this question, we need to find the integral of given function using integration by parts.

Q: Integrate: Stan? (3x) secº (3æ)dx ес

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Q: y = sech /2 + v2x + 1 + tanh v8x² + 3

A: To find the derivative of the function

Q: [xVtan x² sec* x² dx -

A: Given,         ∫xtanx2sec4x2dx

Q: cos(T/x5) dx 16

A: Given that: ∫cos(π/x15)dxx16

Q: dy Solve dx ex +

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Q: 1. Jxe dx

A: We have to apply simple integration rules to solve the problem

Q: dy when x = 0, dx Find

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Q: Solve dy dx + y tan x = -y³x sec²(x)

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Q: 3 4-y y dx dy = 1 2y MIN

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Q: xe dx

A: In the given question we have to solve the integral s.t ∫xexdx. we will solve the indefinite…

Q: Ssin x CosX dx 6x dx

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Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: Sx'sinx 3. 「メさ。 2 X X e

A: solution:-(1)∫x3sinx dxapplying intgration by parts=x3∫sinx dx-∫ddxx3∫sinx dxdx=-x3cosx+∫3x2cosx…

Q: (2y) dy. CSC

A: We will start with the substitution, csc-1(2y) = x and apply the integration by parts. And, will use…

Q: Evaluate the integral.

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

Q: dx wherein x(2) = 4 り dy

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Q: dy Solve: dx cotx = 0

A: Given,  The differential equation  dydx-cotx = 0   We have to solve it

Q: sinh e Incot3x h- dx St 1+9x²

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Q: hy's mea x) = eX

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Q: ) ㅠ S tan5 (2x) sec² (2x) dx 2

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Q: sech x dx , 0 < x < 1

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Q: 3 sinx 19. dx V1-x²

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Q: dx 62 + x² Integrate:

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Q: find dy/dx by implicit differentiation 5x4/5 + 10y6/5 = 15

A: The equation is 5x4/5+10y6/5=15.   Differentiate it with respect to x.…

Q: find dy y = tan-1(ex2)

A: The given equation is y=tan-1ex2. To find the value of dydx. Solution: y=tan-1ex2 differentiate with…

Q: ] Integrate by parts to show that Vx dx = 2e4 - e* dx. ex. е —

A: To evaluate the given integral choose  √x as the first function and ex as the second function and…

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: solve sin2x dy -y=tanx dx

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Q: dr(sec'x) dx

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Q: 2. [ y dy dx carctan3/2 3 secx 3/2

A: Topic  = Integration

Q: dy - (1+x)у -ху? .2 1.) х- dx

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Q: sec“ x (Vtan3 x +1) dx (Vtan3, Px+1) 4

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Q: dx ex sin2 (e

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Q: |tanx dx = -In/secx|+C A In/secx + C B In/cscx +C .C -In/cscx +C D

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Q: calculate the derivative.

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Q: 4. EVALVATE | sin4x vos5x dx

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Q: Integrate x?dx

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Q: 2VIn 3 •VIn 3 35. dx dy ly/2

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Q: +y (cotx) = 5e* dx

A: Given;

Q: Je sin( -4x)dx 3r Su

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Q: Integrate sec5x dx

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Q: (ii) sec2 (x) dx

A: