What is the integral of 3x+1/(3x) ?

The integral of 3x+1/(3x) is (3x^2)/2+1/3 ln|x|+C

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integral of 3x+1/(3x)

\int 3 x + \frac{1}{3 x} d x

\frac{3 x ^{2}}{2} + \frac{1}{3} ln ∣ x ∣ + C

Solution steps

\int 3 x + \frac{1}{3 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 3 x d x + \int \frac{1}{3 x} d x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int \frac{1}{3 x} d x = \frac{1}{3} ln ∣ x ∣

= \frac{3 x ^{2}}{2} + \frac{1}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{3 x ^{2}}{2} + \frac{1}{3} ln ∣ x ∣ + C

y^{^{''}} - 6 y^{^{'}} + 7 y = 0, y (0) = 0, y^{^{'}} (0) = 7

\frac{d}{d x} (x e^{\frac{y}{z}})

7 x - 6 x

\int_{1}^{5} \frac{ln ( x )}{x ^{2}} d x

\frac{d}{d x} (3 x^{4} - 8 x^{3} + 6 x^{2})

What is the integral of 3x+1/(3x) ?
The integral of 3x+1/(3x) is (3x^2)/2+1/3 ln|x|+C