Need Help with Integration? Let Us Solve Your Integral! | I = 5/(3+4sinx)

[CaspianTiger]

I am trying to solve this integral. Any help would be great.

I 5/(3+4sinx)

I tried suddinb t=tan x/2 but it gives me a result of:

=5 I (1+x^2)/(3+11x)

I am not sure what to do with this or if this is the right emthod any help would be great.

Thanks

Using I for integration sign.

 

[tiny-tim]

Hi CaspianTiger!

(have an integral: ∫ )

∫ 5/(3+4sinx)

I tried suddinb t=tan x/2 but it gives me a result of:

=5 ∫ (1+x^2)/(3+11x)

I am not sure what to do with this or if this is the right emthod any help would be great.

Are you sure (1+t²)dt/(3+11t) is right?

Anyway, then you use long division and/or partial fractions.

 

[CaspianTiger]

Hi CaspianTiger!

(have an integral: ∫ )


Are you sure (1+t²)dt/(3+11t) is right?

Anyway, then you use long division and/or partial fractions.

Hmm... I am not sure if this is right. I am just following a method from a book. But it doesn't have an example like this one.

Usually with these problems from the book, you have to use ∫1/x^2+or-a^2

To get the result (1+t2)dt/(3+11t)

I made 3+4sinx = 3+ 8t/(1+t^2)

Then i add them and put them back into the integral. Usually i have a t^2 in the denominator. SO i am confused by this one. The wolf integrator has an insane answer though.

 

[tiny-tim]

I made 3+4sinx = 3+ 8t/(1+t^2)

(just got up :zzz:)

ah, but 3+ 8t/(1+t²) = (3+ 8t + 3t²)/(1+t²)

 

[staredsky]

Greetings,
I'm not so good in integrations, but I tryed to solve it with Mathematica, and I got this answer

(5 I (121 x^2-66 x+260 log(11 x+3)-27))/2662

Hopefully it can help.

 

[CaspianTiger]

(just got up :zzz:)

ah, but 3+ 8t/(1+t²) = (3+ 8t + 3t²)/(1+t²)

What a stupid mistake.

Thanks.