Question

Tìm:

a) \(\int4^xdx;\)                       b) \(\int\dfrac{1}{e^x}dx;\)                        c) \(\int\left(2.3^x-\dfrac{1}{3}.7^x\right)dx.\)

Answer 1

a) \(\int {{4^x}dx}  = \frac{{{4^x}}}{{\ln 4}} + C\);

b) \(\int {\frac{1}{{{e^x}}}dx}  = \int {{{\left( {\frac{1}{e}} \right)}^x}dx}  = \frac{{{{\left( {\frac{1}{e}} \right)}^x}}}{{\ln \frac{1}{e}}} + C =  - {e^{ - x}} + C\);

c) \(\int {\left( {{{2.3}^x} - \frac{1}{3}{{.7}^x}} \right)dx}  = 2\int {{3^x}} dx - \frac{1}{3}\int {{7^x}} dx = \frac{{{{2.3}^x}}}{{\ln 3}} - \frac{{{7^x}}}{{3\ln 7}} + C\).