integral a/(b + c*e^x)

Asked by shikhachaturvedi.talk | 21st Jun, 2015, 07:06: PM

Expert Answer:

integral fraction numerator a over denominator b plus c e to the power of x end fraction d x equals integral fraction numerator a e to the power of x over denominator b e to the power of x plus c e to the power of 2 x end exponent end fraction d x S u b s t i t u t e space e to the power of x equals t comma space e to the power of x d x equals d t. space T h e space i n t e g r a l space b e c o m e s integral fraction numerator a over denominator b t plus c t squared end fraction d t equals a integral fraction numerator d t over denominator c open parentheses t squared plus begin display style b over c end style t plus open parentheses begin display style fraction numerator b over denominator 2 c end fraction end style close parentheses squared minus open parentheses fraction numerator b over denominator 2 c end fraction close parentheses squared close parentheses end fraction equals a over c integral fraction numerator d t over denominator open parentheses t plus begin display style fraction numerator b over denominator 2 c end fraction end style close parentheses squared minus open parentheses fraction numerator b over denominator 2 c end fraction close parentheses squared end fraction equals a over c cross times fraction numerator 1 over denominator 2 open parentheses fraction numerator b over denominator 2 c end fraction close parentheses end fraction ln open vertical bar fraction numerator t plus fraction numerator b over denominator 2 c end fraction minus fraction numerator b over denominator 2 c end fraction over denominator t plus fraction numerator b over denominator 2 c end fraction plus fraction numerator b over denominator 2 c end fraction end fraction close vertical bar plus C equals a over b ln open vertical bar fraction numerator t over denominator t plus b over c end fraction close vertical bar plus C equals a over b ln open vertical bar fraction numerator c e to the power of x over denominator c e to the power of x plus b end fraction close vertical bar plus C

Answered by satyajit samal | 22nd Jun, 2015, 01:54: AM