Question

Tìm:

a) \(\int4^{x+2}dx;\)

b) \(\int\left(5^{x+2}-e^{x+1}\right)dx\).

Answer 1

a) \(\int {{4^{x + 2}}dx} = \int {{4^x}{{.4}^2}dx} = 16\int {{4^x}dx} = 16.\frac{{{4^x}}}{{\ln 4}} + C = \frac{{{4^{x + 2}}}}{{\ln 4}} + C\).

b) \(\int {({5^{x + 2}} - {e^{x + 1}})dx} = \int {({5^x}{{.5}^2} - {e^x}.e)dx} = 25\int {{5^x}dx} - e\int {{e^x}dx} \)

\(= 25\frac{{{5^x}}}{{\ln 5}} - e\frac{{{e^x}}}{{\ln e}} + C = \frac{{{5^{x + 2}}}}{{\ln 5}} - {e^{x + 1}} + C\).