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evaluate ∫ ( 2^x + 5/x – 1/x^1/3) dx

evaluate
∫ ( 2^x + 5/x –  1/x^1/3) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int (2^{x} + \frac{5}{x} + \frac{1}{x^{1/3}})dx
I = \int 2^{x}dx + \int \frac{5}{x}dx + \int \frac{1}{x^{1/3}}dx
I = \frac{2^{x}}{ln2} + 5ln(x) + \int x^{-1/3}dx
I = \frac{2^{x}}{ln2} + 5ln(x) + \frac{x^{-1/3+1}}{-1/3+1} + constant
I = \frac{2^{x}}{ln2} + 5ln(x) + \frac{x^{2/3}}{2/3} + constant
I = \frac{2^{x}}{ln2} + 5ln(x) + \frac{3x^{2/3}}{2} + constant

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