Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\int ( \frac { \sin x - \cos x } { 3 \sin x - \sin 3 x } ) e ^ { x } d x$$

Answer

$$(IM*n*t^2*e^(2+x)*g*r*a*d*x*(sin(x)-cos(x)))/(3*sin(x)-sin(3*x))$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\imath ntegrate(\sin{x}-\cos{x}){e}^{x}dx}{3\sin{x}-\sin{3x}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{\imath n{t}^{2}{e}^{2+x}gra(\sin{x}-\cos{x})dx}{3\sin{x}-\sin{3x}}\]
Regroup terms.
\[\frac{\imath n{t}^{2}{e}^{2+x}gradx(\sin{x}-\cos{x})}{3\sin{x}-\sin{3x}}\]
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