# Math Help - integration

1. ## integration

Express in terms of and .
Hence evaluate .

How would you solve this question?

2. Hello,
Originally Posted by Haris
Express in terms of and .
Hence evaluate .

How would you solve this question?
We know that $\cosh(x-y)={\color{red}\cosh(x)\cosh(y)}-\sinh(x)\sinh(y)$ and $\cosh(x+y)={\color{red}\cosh(x)\cosh(y)}+\sinh(x)\ sinh(y)$

$\cosh(x-y)+\cosh(x+y)=2 \cosh(x)\cosh(y)$

Hence $-\cosh(x)\cosh(y)=-\frac 12 (\cosh(x-y)+\cosh(x+y))$

Let y=2x and transform your integral.

3. $
\int-cosh(x)cosh(2x)dx
$

$=-\frac{1}{2} \int cosh(3x)+cosh(-x)dx$

$=\frac{1}{2}sinh(-x)-\frac{1}{6}sinh(3x)+C$

Is this correct?

4. Originally Posted by Haris
$
\int-cosh(x)cosh(2x)dx
$

$=-\frac{1}{2} \int cosh(3x)+cosh(-x)dx$

$=\frac{1}{2}sinh(-x)-\frac{1}{6}sinh(3x)+C$

Is this correct?
Yes

But remember that sinh is an odd function and hence $\sinh(-x)=-\sinh(x)$