Integration Coursework

**smwatson** · November 13th 2008, 10:32 AM

Find

$\int (1+tan(x))/(1+cos(x)) dx$

and

$\int (1+tanh(x))/(1+cosh(x)) dx$

**Math_Helper** · November 13th 2008, 11:33 AM

**Moo** · November 13th 2008, 11:43 AM

Hello,

It is pretty straightforward if you use Weierstrass substitution :

$t=\tan^2 \frac x2$

$\cos(x)=\frac{1-t^2}{1+t^2}$

$\sin(x)=\frac{2t}{1+t^2}$

$\tan(x)=\frac{2t}{1-t^2}$

and $dx=\frac{2}{1+t^2} ~ dt$

**Mathstud28** · November 13th 2008, 01:22 PM

Originally Posted by smwatson

Find

$\int (1+tan(x))/(1+cos(x)) dx$

$\int\frac{1+\tan(x)}{1+\cos(x)}dx=\int\bigg[\frac{1}{\cos(x)+1}-\frac{\sin(x)}{\cos(x)(\cos(x)+1)}\bigg]dx$

**Krizalid** · November 13th 2008, 01:36 PM

$\begin{aligned}<br /> \int{\frac{1+\tan x}{1+\cos x}\,dx}&=\int{\frac{(1+\tan x)(1-\cos x)}{\sin ^{2}x}\,dx} \\ <br /> & =\int{(1+\tan x)\left( \csc ^{2}x-\cot x\csc x \right)\,dx} \\ <br /> & =\int{\csc ^{2}x\,dx}-\int{\cot x\csc x\,dx}+\int{\frac{dx}{\sin x\cos x}}-\int{\csc x\,dx}.<br /> \end{aligned}$

Each one of these are pretty staightforward to make.

Thread: Integration Coursework

LinkBack

Thread Tools

Display

Integration Coursework

Similar Math Help Forum Discussions

Coursework help

AS coursework, Ideas?

Real problem with this coursework

maths coursework for tommorrow

Coursework Help Nth Term!!!

Search Tags