Integrating Cosine and sine integrals by substitution

Hi all,

I have a few integrals that I have been asked to evaluate using integration by substitution. I have never came across anything like this before.

For example;

Integrate (1+sinx)/cosx by integration.

Is it possible. I know how to integrate other forms of integrals by substitution for example involving x's.

Thanks.

Re: Integrating Cosine and sine integrals by substitution

Looks like I am getting some where.

Let u = 1+sinx, du/dx = cosx, du = cosxdx

I am supposed to write everything in terms of u. But to replace **cosxdx** the other cosx to replace is a fraction of 1/cosx

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Googl** Hi all,

I have a few integrals that I have been asked to evaluate using integration by substitution. I have never came across anything like this before.

For example;

Integrate (1+sinx)/cosx by integration.

Is it possible. I know why integrate other forms of integrals by substitution for example involving x's.

Thanks.

Dear Googl,

Substitute,

Re: Integrating Cosine and sine integrals by substitution

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Googl** Hi all,

I have a few integrals that I have been asked to evaluate using integration by substitution. I have never came across anything like this before.

For example;

Integrate (1+sinx)/cosx by integration.

Is it possible. I know why integrate other forms of integrals by substitution for example involving x's.

Thanks.

I'm sure you can go from here...

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Sudharaka** Dear Googl,

Substitute,

Could you continue a bit further. The problem is that du results in cosxdx.

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Prove It**
I'm sure you can go from here...

Why did you multiply by (1 - sinx) at the beginning?

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Googl** Could you continue a bit further. The problem is that du results in cosxdx.

Dear Googl,

Hope this will help you.

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Googl** Looks like I am getting some where.

Let u = 1+sinx, du/dx = cosx, du = cosxdx

I am supposed to write everything in terms of u. But to replace **cosxdx** the other cosx to replace is a fraction of 1/cosx

Your substitution can also be used. Try to write cos x in terms of u and substitute it as I had done in my previous post. Hope you can continue.

Re: Integrating Cosine and sine integrals by substitution

Quote:

Originally Posted by

**Googl** Why did you multiply by (1 - sinx) at the beginning?

Because it's easier to make sure you have a single sine or cosine in the numerator, so that it can become part of your ...

Re: Integrating Cosine and sine integrals by substitution

I will think through your examples and get back to you.

Thanks.

Re: Integrating Cosine and sine integrals by substitution

straight-forward integration ...