Example

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

Question

$$-\int\frac{1}{1+x^{2}}\cdot e^{-ln(1+x)}$$

Answer

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

Solution


Remove parentheses.
\[-\imath ntegrate\times \frac{1}{1+{x}^{2}}{e}^{-\ln{(1+x)}}dx\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[-\imath ntegrate\times \frac{1}{1+{x}^{2}}\times \frac{1}{{e}^{\ln{(1+x)}}}dx\]
Simplify  \({e}^{\ln{(1+x)}}\)  to  \(1+x\).
\[-\imath ntegrate\times \frac{1}{1+{x}^{2}}\times \frac{1}{1+x}dx\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[-\frac{\imath ntegrate\times 1\times 1\times dx}{(1+{x}^{2})(1+x)}\]
Regroup terms.
\[-\frac{nttgradx\imath ee}{(1+{x}^{2})(1+x)}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[-\frac{n{t}^{2}gradx\imath {e}^{2}}{(1+{x}^{2})(1+x)}\]
Regroup terms.
\[-\frac{{e}^{2}\imath n{t}^{2}gradx}{(1+{x}^{2})(1+x)}\]
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