Let Express the value of in terms of I. pn/12 0 tan ¹2 (2x) sec (2x) dx I = p/12 10 S tan ¹0 (2x) sec (2x) dx. 0 π/12 12 tan ¹2 (2x) sec (2x) dx

Q: S sin? (x)cos(x)dx

A: Let the given integral be y - y = ∫sin2(x)cos(x)dxLett = sinxdtdx = cosxdt = cosxdxSubstituting…

Q: 6 tan (10x) dx

A:

Q: /4 tan x dx /4

A:

Q: Evaluate ㅠ * 0 sin (9x) sin(5x) dx.

A: To evaluate the following integral.∫0π sin9x sin5x dx

Q: Tan (  pi/2 - x ) =

A:

Q: I/3 1 dx Ja16 \1+ tanx. R/6

A: SOLUTION:Given let   I = ∫π6π311+tan xdx= ∫π6π3cos xcos x+sin xdx=12∫π6π32cos xcos x+sin…

Q: ] 1 1-x² dx = tan¹(x)

A:

Q: Derive the formula tan¯¹(x) =_¹. dx 1+x²

A: Introduction: The derivative of a function is defined as the instantaneous rate of change of a…

Q: π/4 IF ST/A tan (x) sec(x) dx = I, express the value of 。 π/4 tan (x) sec(x) dx in terms of I.

A: Given:- ∫0π4tan4xsecxdx=I

Q: T/6 6 tan 2x dx

A: In this question, we need to evaluate the given integral.

Q: I sec25x dx = ? tan x +C 1/5 tan x +c 1/5 tan 8x +C

A: We will solve the problem

Q: True or false: For any constant C, d =[ tan(x) + C] = [sec(x)]² dx

A: The objective of the question is to verify whether the derivative of the function tan(x) + C equals…