Transforming trigonometric integrands

**reiward** · December 12th 2011, 03:13 PM

Hi,

I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.

Thank you.

**Prove It** · December 12th 2011, 03:23 PM

Originally Posted by reiward

Hi,

I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.

Thank you.

$\displaystyle \begin{align*} \int{\frac{3\cos{x} - 4}{\sin^2{x}}\,dx} &= \int{\frac{3\cos{x}}{\sin^2{x}}\,dx} - \int{\frac{4}{\sin^2{x}}\,dx} \\ &= \int{\frac{3\cos{x}}{\sin^2{x}}\,dx} - \int{4\csc^2{x}\,dx}\end{align*}$

Solve the first using the substitution $\displaystyle \begin{align*} u = \sin{x} \implies du = \cos{x}\,dx \end{align*}$ and for the second, what is the derivative of $\displaystyle \begin{align*} \cot{x} \end{align*}$ ?

**Prove It** · December 12th 2011, 03:25 PM

Originally Posted by reiward

Hi,

I am having trouble at transforming trigonometric integrands. I just need these to be transformed then I think I will be able to integrate it. I hope you can help me.

Thank you.

$\displaystyle \begin{align*} \int{\left(3 - \csc^2{y}\right)\cos{y}\,dy} &= \int{\left(3 - \frac{1}{\sin^2{y}}\right)\cos{y}\,dy} \end{align*}$

Now make the substitution $\displaystyle \begin{align*} u = \sin{y} \implies du = \cos{y}\,dy \end{align*}$ .

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