Nguyên hàm(16).

Question

Tính nguyên hàm: $$\int\dfrac{e^{2x}+2^{2x}\times 3^x}{e^{3x}}dx$$

khangnguyenthanh · Answer 1 · 11/29/2013 11:41:21 PM

Ta có:

$\int\dfrac{e^{2x}+2^{2x}\times 3^x}{e^{3x}}dx$

$=\int\left(e^{-x}+\left(\dfrac{12}{e^3}\right)^x\right)dx$

$=-e^{-x}+\dfrac{1}{\ln\frac{12}{e^3}}\left(\dfrac{12}{e^3}\right)^x+C$

$=-e^{-x}+\dfrac{1}{\ln12-3}\left(\dfrac{12}{e^3}\right)^x+C$

Trả lời 29-11-13 11:41 PM

khangnguyenthanh
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