Question

Tìm:

a) \(\int x^5dx;\)                  b) \(\int\dfrac{1}{\sqrt[3]{x^2}}dx\) (x > 0);                   c) \(\int7^x\);                  d) \(\int\dfrac{3^x}{5^x}dx\).

 

Answer 1

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

b) \(\int {\frac{1}{{\sqrt[3]{{{x^2}}}}}dx} = \int {\frac{1}{{{x^{\frac{2}{3}}}}}dx}  = \int {{x^{ - \frac{2}{3}}}dx = \frac{{{x^{\frac{1}{3}}}}}{{\frac{1}{3}}} + C = 3\sqrt[3]{x} + C} \).

c) \(\int {{7^x}dx}  = \frac{{{7^x}}}{{\ln 7}} + C\).

d) \(\int {\frac{{{3^x}}}{{{5^x}}}dx}  = \int {{{\left( {\frac{3}{5}} \right)}^x}dx}  = \frac{{{{\left( {\frac{3}{5}} \right)}^x}}}{{\ln \frac{3}{5}}} + C\).