Example

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

Question

$$\int\frac{e^{arctg\ x}+x\ ln(1+x^{2})+1}{1+x^{2}}dx$$

Answer

$$(e^2*IM*n*t^2*g*r*a*d*x*(e^(a*r*c*tan(x))+x*ln(1+x^2)+1))/(1+x^2)$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\imath ntegrate({e}^{arc\tan{x}}+x\ln{(1+{x}^{2})}+1)dx}{1+{x}^{2}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{\imath n{t}^{2}{e}^{2}gra({e}^{arc\tan{x}}+x\ln{(1+{x}^{2})}+1)dx}{1+{x}^{2}}\]
Regroup terms.
\[\frac{{e}^{2}\imath n{t}^{2}gradx({e}^{arc\tan{x}}+x\ln{(1+{x}^{2})}+1)}{1+{x}^{2}}\]
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