"Evaluate the integral. ∫(2x3+1x)dx" solved and explained - Plainmath

generals336

Answered question

2021-01-15

Evaluate the integral.

\int (\frac{2}{x^{3}} + \frac{1}{\sqrt{x}}) d x

Answer & Explanation

Elberte

Skilled2021-01-16Added 95 answers

Given That

\int (\frac{2}{x^{3}} + \frac{1}{\sqrt{x}}) d x

= 2 [\frac{x^{- 3 + 1}}{- 3 + 1}] + [\frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}] + c [∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c]

= - \frac{2}{2} x^{- 2} + 2 \sqrt{x} + c

= - \frac{1}{x^{2}} + 2 \sqrt{x} + c

∴ \int (\frac{2}{x^{3} + \frac{1}{\sqrt{x}}}) d x = - \frac{1}{x^{2}} + 2 \sqrt{x} + c

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