Question

Find ∫ ln 3𝑥 − 1 𝑥 5 + cos 4𝑥 − 𝑒 −𝑥 2 ⁄ 𝑑x

Answer 1

$\int ln(3x) -x^5 +cos(4x) -e^{\dfrac{-x}{2}}$

$\int 1\times ln(3x) -x^5 +cos(4x) -e^{\dfrac{-x}{2}}$

$[ln(3x)x-\int x \times \dfrac{1}{x} ] +\dfrac{sin(4x)}{4}-{ \dfrac{x^6}{6} } -(-2e^{\dfrac{-x}{2}})$

$xln(3x)- x +\dfrac{sin(4x)}{4}-{ \dfrac{x^6}{6} } +2e^{\dfrac{-x}{2}} +C$