`int (x^2 + 2^(-x)) dx` Find the indefinite integral

Wednesday, December 5, 2012

$\displaystyle\int{\left({{x}}^{{2}}+{{2}}^{{-{x}}}\right)}{\left.{d}{x}\right.}$ Find the indefinite integral

Indefinite integral is additive, i.e. $\displaystyle\int{\left({f{+}}{g}\right)}=\int{f{+}}\int{g{.}}$ Therefore

$\displaystyle\int{\left({{x}}^{{2}}+{{2}}^{{-{x}}}\right)}{\left.{d}{x}\right.}=\int{{x}}^{{2}}{\left.{d}{x}\right.}+\int{{2}}^{{-{x}}}{\left.{d}{x}\right.}.$

Both integrals are table ones or very close to them, so the answer is

$\displaystyle\frac{{{x}}^{{3}}}{{3}}-\frac{{1}}{{\ln{{\left({2}\right)}}}}{{2}}^{{-{x}}}+{C},$

where $\displaystyle{C}$ is an arbitrary constant.

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Wednesday, December 5, 2012

$\displaystyle\int{\left({{x}}^{{2}}+{{2}}^{{-{x}}}\right)}{\left.{d}{x}\right.}$ Find the indefinite integral

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Wednesday, December 5, 2012

Find the indefinite integral

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Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle\int{\left({{x}}^{{2}}+{{2}}^{{-{x}}}\right)}{\left.{d}{x}\right.}$ Find the indefinite integral

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?