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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

Popular Examples

integral from 0 to 27 of 5/(x^{2/3)}

\int_{0}^{27} \frac{5}{x ^{\frac{2}{3}}} d x

y^'=3x+y,y(0)=2

y^{^{'}} = 3 x + y, y (0) = 2

integral of sqrt(x^2+5)

\int x^{2} + 5 d x

limit as r approaches 0 of sin^2(r)

r \to 0 lim (sin^{2} (r))

derivative of (2-3x^3)^{-2}derivative of

(2 - 3 x^{3})^{- 2}

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