Pertanyaan

Tentukan nilai

Tentukan nilai $begin mathsize 14px style integral fraction numerator 3 x plus 2 over denominator square root of x end fraction text d end text x end style$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style integral fraction numerator 3 x plus 2 over denominator square root of x end fraction text d end text x end style$ $begin mathsize 14px style equals integral fraction numerator 3 x over denominator square root of x end fraction d x plus integral fraction numerator 2 over denominator square root of x end fraction d x end style$

$begin mathsize 14px style equals 3 integral x to the power of 1 minus 1 half end exponent d x plus 2 integral x to the power of negative 1 half end exponent d x equals 3 integral x to the power of 1 half end exponent d x plus 2 open parentheses fraction numerator 1 over denominator negative begin display style 1 half end style plus 1 end fraction x to the power of negative 1 half plus 1 end exponent close parentheses plus C equals 3 open parentheses fraction numerator 1 over denominator begin display style 1 half plus 1 end style end fraction x to the power of 1 half plus 1 end exponent close parentheses plus 2 open parentheses fraction numerator 1 over denominator begin display style 1 half end style end fraction x to the power of 1 half end exponent close parentheses plus C equals 3 open parentheses fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction x to the power of 3 over 2 end exponent close parentheses plus 2 open parentheses 2 x to the power of 1 half end exponent close parentheses plus C equals 3 open parentheses 2 over 3 x to the power of 3 over 2 end exponent close parentheses plus 4 x to the power of 1 half end exponent plus C equals 2 x to the power of 3 over 2 end exponent plus 4 square root of x plus C end style$