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Zadatak 0031

Test: MPsIVKVIII_006

 

Reši integrale: a) \(\int \left (x ^{6}-\sqrt[5]{x}+\frac{1}{x^3} \right )dx\);  b) \(\int \frac{2\cos ^{2}+1}{\cos ^{2}x}dx\).

 

Rešenje:


 

a) \(...=\int x^6dx-\int x^{\frac{1}{5}}dx+\int x^{-3}dx\)\(=\int x^6dx-\int x^{\frac{1}{5}}dx+\int x^{-3}dx\)

 

\(=\frac{x^7}{7}-\frac{x^\frac{6}{5}}{\frac{6}{5}}-\frac{x^{-2}}{2}+C\)\(=\frac{x^7}{7}-\frac{5x^\frac{6}{5}}{6}-\frac{1}{2x^2}+C\)

 

b) \(...=\int \left ( \frac{2\cos ^2x}{\cos ^2x}+\frac{1}{\cos ^2x} \right )dx\)

 

\(=\int dx+\int \frac{1}{\cos ^2x}dx=x+\tan x+C\).


 

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