Integration. help please (1 Viewer)

[NizDiz]

Hi peeps, i just started volumes and have all this integration h/w due in the next week or so and on top of that i have volumes homework due on tuesday, which i am on top of. can u guys help me out on these integration questions (i've forgotten a lot of it).

Integral of

1. tan^-1(2x) dx
2. x^3 dx / x^2+1
3. dx / (x^2)*((1-x^2)^1/2)
4. dx / x*(a^2+x^2)^1/2
5. same as 4 but minus, (a^2-x^2)^1/2 the difference
6. same as 5 but x and a switched around
7. x dx / 1+x^1/2
8. cos^-1(x) dx / (1-x^2)^1/2
9. dx / x(log x)^3
10. sec^4(3x) dx
11. dx / x^2 (1-x)

Sorry for inconvenience guys, but i really need to get this done and i missed a bit of this at the start so im in catch up mode now and its bloody hard. Help will be much appreciated. cheers

 

[Trebla]

Hi peeps, i just started volumes and have all this integration h/w due in the next week or so and on top of that i have volumes homework due on tuesday, which i am on top of. can u guys help me out on these integration questions (i've forgotten a lot of it).

Integral of

1. tan^-1(2x) dx
2. x^3 dx / x^2+1
3. dx / (x^2)*((1-x^2)^1/2)
4. dx / x*(a^2+x^2)^1/2
5. same as 4 but minus, (a^2-x^2)^1/2 the difference
6. same as 5 but x and a switched around
7. x dx / 1+x^1/2
8. cos^-1(x) dx / (1-x^2)^1/2
9. dx / x(log x)^3
10. sec^4(3x) dx
11. dx / x^2 (1-x)

Sorry for inconvenience guys, but i really need to get this done and i missed a bit of this at the start so im in catch up mode now and its bloody hard. Help will be much appreciated. cheers

I'll just note the techniques that you can use
1. Integration by parts
2. Polynomial long division/manipulation then partial fractions
3. Substitution x = sin θ
4. Substitution x = a tan θ
5. Substitution x = a sin θ
6. Substitution x = a sec θ
7. Substitution u = 1 + x^1/2
8. Reverse chain rule or just use substitution u = cos^-1x
9. Reverse chain rule or just use substitution u = log x
10. Note that sec⁴3x = sec²3x sec²3x = sec²3x (1 + tan²3x) = sec²3x + sec²3x tan²3x. The second expression can be found by reverse chain rule or substitution u = tan 3x
11. Partial fractions or some numerator manipulation

 

[Registered User]

You can check your answers here: http://www.wolframalpha.com/

 

[NizDiz]

thank you people, this will help get speed up my work legends!!