Tentukan nilai ∫(2x1+x2−ex)dx

Pertanyaan

Tentukan nilai $begin mathsize 14px style integral open parentheses fraction numerator 1 over denominator 2 x end fraction plus x squared minus e to the power of x close parentheses straight d x end style$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style integral subscript blank open parentheses fraction numerator 1 over denominator 2 x end fraction plus x squared minus e to the power of x close parentheses d x equals integral subscript blank fraction numerator 1 over denominator 2 x end fraction d x plus integral subscript blank x squared d x minus integral subscript blank e to the power of x d x end style$

$size 14px equals size 14px 1 over size 14px 2 size 14px ln begin mathsize 14px style left parenthesis open vertical bar x close vertical bar right parenthesis end style size 14px plus fraction numerator size 14px 1 over denominator size 14px 2 size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px 2 size 14px plus size 14px 1 end exponent size 14px minus size 14px e to the power of size 14px x size 14px plus size 14px C size 14px equals size 14px 1 over size 14px 2 size 14px ln begin mathsize 14px style left parenthesis open vertical bar x close vertical bar right parenthesis end style size 14px plus size 14px 1 over size 14px 3 size 14px x to the power of size 14px 3 size 14px minus size 14px e to the power of size 14px x size 14px plus size 14px C$