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# P3 Integration watch

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1. Integrate with respect to x:

1) (x+2) / x(x-1)

2) (sec^2 x) / (1+tanx)^3

3) sin^2 2x

4) x^2 / (x-2)

5) (sinx + 2cosx)^2

1) 3ln(x-1) - 2ln(x)
2) - 0.5 (1+tanx)^ -2
3) 0.5x - 0.125sin4x
4) 0.5x^2 + 2x + 4 ln(x-2)
5) 2.5x + 0.75sin2x - cos2x.

Cheers
2. 1) (x+2)/x(x-1) = 3/(x-1)-2/x (partial fractions)
∫f(x)dx=3ln|x-1|-2ln|x|+C

2) ∫sin²2x.dx = ∫(½-½cos4x).dx = ½x-1/8sin4x +C

3) sec²x/(1+tanx)³
u=1+tanx => du/dx=sec²x => du=sec²x.dx
=> ∫sec²x/(1+tanx)³dx = ∫u^-3.du = -½u^-2+C
3. Hi,

Referring to the 5 questions below. I am offering to do these questions for you for free and any other in future for only £25/ year. Mod Edit - Link removed

1) (x+2) / x(x-1)

2) (sec^2 x) / (1+tanx)^3

3) sin^2 2x

4) x^2 / (x-2)

5) (sinx + 2cosx)^2

Ernest
4. 2. Use the substitution u=1+tanx with du=sec²x dx.
3. Use the identity cos4x = 1 - 2sin²2x.
4. Use long division to split it into proper fractions.
5. (sinx + 2cosx)^2 = sin²x + 2(2sinxcosx) + 4cos²x = 1 + 2sin2x + 3cos²x. Now use a variant of the identity used in 3 to integrate cos²x.
5. ernmaths, I seriously doubt you will find any customers here, seeing as many members will do what you're offering for free.

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