Find the indefinite integral of the given function :

                  (e^x) / x

Asked by shamiikhullah.akram18 | 31st Aug, 2019, 01:46: AM

Expert Answer:

e to the power of x equals 1 plus fraction numerator x over denominator 1 factorial end fraction plus fraction numerator x squared over denominator 2 factorial end fraction plus fraction numerator x cubed over denominator 3 factorial end fraction plus....
integral e to the power of x over x d x equals integral 1 over x open parentheses 1 plus fraction numerator x over denominator 1 factorial end fraction plus fraction numerator x squared over denominator 2 factorial end fraction plus fraction numerator x cubed over denominator 3 factorial end fraction plus.... close parentheses d x
equals integral open parentheses 1 over x plus 1 plus fraction numerator x over denominator 2 factorial end fraction plus fraction numerator x squared over denominator 3 factorial end fraction plus.... close parentheses d x
equals ln x plus fraction numerator x over denominator 1 factorial end fraction plus fraction numerator x squared over denominator 2 cross times 2 factorial end fraction plus fraction numerator x cubed over denominator 3 cross times 3 factorial end fraction plus....
equals ln x plus sum from n equals 1 to infinity of fraction numerator x to the power of n over denominator n times n factorial end fraction

Answered by Renu Varma | 3rd Sep, 2019, 12:13: PM

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