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Popular >

integral of (3/x+x)

Solution

\int (\frac{3}{x} + x) d x

Solution

3 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

Solution steps

\int \frac{3}{x} + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{3}{x} d x + \int x d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int x d x = \frac{x ^{2}}{2}

= 3 ln ∣ x ∣ + \frac{x ^{2}}{2}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{x ^{2}}{2} + C

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k = 1 \sum \infty 8 (\frac{1}{5})^{k}

Frequently Asked Questions (FAQ)

What is the integral of (3/x+x) ?
The integral of (3/x+x) is 3ln|x|+(x^2)/2+C