aluate 9/ sin(x) cos(x) dx by four methods.

Q: 7 cos?(x) sin(2x) dx

A:

Q: 3 4) Find / sin (2x) cos (2x)dx

A:

Q: dr/dθ= cos (-5πθ), r(0)=9

A: Given,

Q: x" cos h(x) dx

A:

Q: sin(x)ecos dx COS X 8.

A: Given,

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

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

Q: sin(3x)e°*dx

A:

Q: 0·1 sin(x)dx X

A: Use the nonelementary integral:

Q: (e) sin(2x) sin(x) dx.

A: ∫sin2xsinxdx

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

A:

Q: 37/2 8 cos x dx T/2

A:

Q: 1/4 (sin x + sin x cos x) dx 0.

A: given

Q: sin (x² 3/2 +2)dx

A: See the details solution in below

Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: d(tan(x)) Using Euler’ formula, show that dx cos x 1.

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: d83 da83

A: As per guidelines We"ll answer the first question if multiple questions are given.     Given…

Q: dx dx 1 sin?x +cos²x

A: given that ∫0π2 dxsin2x+14cos2x calculate the integral under the limits 0, π2

Q: (e) /s sin (x) cos (x) dx

A:

Q: S (|sin x| + sin æ') dx

A:

Q: •π/2 (cos x - sin x) dx

A:

Q: S cos(7x) cos (18x)dx

A:

Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

A:

Q: Find sin(a), given that cos(a) = 2/5 and sin(a) < 0.

A: As we know that, the trigonometric identity: sin2θ+cos2θ=1 Given: cosa=25

Q: 7/2 SAT sin" x cos3 x dx

A:

Q: ㅠ (2 cos x - 2 sin x) dx

A:

Q: /3 dx cos x tan x /4

A:

Q: e2x sin(5x) dx

A: Given,  ∫e2x sin(5x) dx

Q: 1/2 cos ¹ x dx

A: The integration of the integral is cos-1x, limit from 0 to 1/2.

Q: x2 Q1 (x sin x+cos x) -dx

A: For integrating the given integral we will use the below-mentioned integration formulas…