Toán tìm nguyên hàm của hàm số: a. f(x)=2^(3x).3^(2x) b. ∫(2+x)^8.xdx 14/11/2021 By Amaya tìm nguyên hàm của hàm số: a. f(x)=2^(3x).3^(2x) b. ∫(2+x)^8.xdx
$\begin{array}{l}a)\quad \displaystyle\int 2^{3x}.3^{2x}dx\\ =\displaystyle\int 8^{x}.9^{x}dx\\ =\displaystyle\int72^xdx\\ =\dfrac{72^x}{\ln72} + C\\ b)\quad \displaystyle\int(2+x)^8xdx\\ Đặt\,\,u = x+2\\ \to du = dx\\ \text{Ta được:}\\ \quad \displaystyle\int(u-2)u^8du\\ = \displaystyle\int u^9du – 2\displaystyle\int u^8du\\ = \dfrac{u^{10}}{10} – \dfrac{2u^9}{9} +C\\ = \dfrac{(x+2)^{10}}{10} – \dfrac{2(x+2)^9}{9} +C \end{array}$ Trả lời
$\begin{array}{l}a)\quad \displaystyle\int 2^{3x}.3^{2x}dx\\ =\displaystyle\int 8^{x}.9^{x}dx\\ =\displaystyle\int72^xdx\\ =\dfrac{72^x}{\ln72} + C\\ b)\quad \displaystyle\int(2+x)^8xdx\\ Đặt\,\,u = x+2\\ \to du = dx\\ \text{Ta được:}\\ \quad \displaystyle\int(u-2)u^8du\\ = \displaystyle\int u^9du – 2\displaystyle\int u^8du\\ = \dfrac{u^{10}}{10} – \dfrac{2u^9}{9} +C\\ = \dfrac{(x+2)^{10}}{10} – \dfrac{2(x+2)^9}{9} +C \end{array}$