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[buithihatien]

tìm nguyên hàm $\int \frac{x+1}{\sqrt{2x+1}}.e^{x}dx$

Edited by buithihatien, 29-01-2019 - 23:47.

[tritanngo99]

tìm nguyên hàm $\int \frac{x+1}{\sqrt{2x+1}}.e^{x}dx$

Ta có: $\int \frac{(x+1)e^x}{\sqrt{2x+1}}dx$

$=\int (\frac{e^x}{2\sqrt{2x+1}}+\frac{(2x+1)e^x}{2\sqrt{2x+1}})dx$

$=\int (\frac{e^x}{2\sqrt{2x+1}}+\frac{e^x\sqrt{2x+1}}{2})dx$

$=\frac{e^{x}\sqrt{2x+1}}{2}+C$