Answer to Question #203414 in Calculus for Rajay Myrie

Question #203414

Find ∫ ln 3π‘₯ βˆ’ 1 π‘₯ 5 + cos 4π‘₯ βˆ’ 𝑒 βˆ’π‘₯ 2 ⁄ 𝑑x


1
Expert's answer
2021-06-07T18:39:03-0400

∫ln(3x)βˆ’x5+cos(4x)βˆ’eβˆ’x2\int ln(3x) -x^5 +cos(4x) -e^{\dfrac{-x}{2}}


∫1Γ—ln(3x)βˆ’x5+cos(4x)βˆ’eβˆ’x2\int 1\times ln(3x) -x^5 +cos(4x) -e^{\dfrac{-x}{2}}


[ln(3x)xβˆ’βˆ«xΓ—1x]+sin(4x)4βˆ’x66βˆ’(βˆ’2eβˆ’x2)[ln(3x)x-\int x \times \dfrac{1}{x} ] +\dfrac{sin(4x)}{4}-{ \dfrac{x^6}{6} } -(-2e^{\dfrac{-x}{2}})


xln(3x)βˆ’x+sin(4x)4βˆ’x66+2eβˆ’x2+Cxln(3x)- x +\dfrac{sin(4x)}{4}-{ \dfrac{x^6}{6} } +2e^{\dfrac{-x}{2}} +C


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