01.20.2017. Friday
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 Mathematical analysis Important functions⦿ Linear polynomial function⦿ Quatratic polynomial function⦿ Cubic polynomial function⦿ Rational function⦿ Root function with even radical⦿ Root function with odd radical⦿ Exponential function⦿ Logarithmic function⦿ Sine function⦿ Cosine function⦿ Tangent function⦿ Cotangent function⦿ Absolute value functions Dervation⦿ Table of Derivatives ⦿ Differentiation rules Integration⦿ Table of Integrals⦿ Integration Rules

Integration

# Table of Integrals

$\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+C,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}n\ne -1$
$\int \frac{1}{x}dx=ln|x|+C$
$\int {e}^{x}dx={e}^{x}+C$
$\int {a}^{x}dx=\frac{{a}^{x}}{ln\phantom{\rule{thinmathspace}{0ex}}a}+C$
$\int cos\phantom{\rule{thinmathspace}{0ex}}xdx=sin\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int sin\phantom{\rule{thinmathspace}{0ex}}xdx=-cos\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int tg\phantom{\rule{thinmathspace}{0ex}}xdx=-ln|cos\phantom{\rule{thinmathspace}{0ex}}x|+C$
$\int ctg\phantom{\rule{thinmathspace}{0ex}}xdx=ln|sin\phantom{\rule{thinmathspace}{0ex}}x|+C$
$\int \frac{1}{co{s}^{2}\phantom{\rule{thinmathspace}{0ex}}x}dx=tg\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{si{n}^{2}\phantom{\rule{thinmathspace}{0ex}}x}dx=-ctg\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{1+{x}^{2}}dx=arctg\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{\sqrt{1-{x}^{2}}}dx=arcsin\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int sh\phantom{\rule{thinmathspace}{0ex}}xdx=ch\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int ch\phantom{\rule{thinmathspace}{0ex}}xdx=sh\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{\sqrt{{x}^{2}+1}}dx=arsh\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{\sqrt{{x}^{2}-1}}dx=arch\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{c{h}^{2}\phantom{\rule{thinmathspace}{0ex}}x}dx=th\phantom{\rule{thinmathspace}{0ex}}x+C$
$\int \frac{1}{s{h}^{2}\phantom{\rule{thinmathspace}{0ex}}x}dx=-cth\phantom{\rule{thinmathspace}{0ex}}x+C$