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Popular >

integral of 3+1/x

Solution

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

Solution

3 x + ln ∣ x ∣ + C

Solution steps

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

\int 3 d x = 3 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 x + ln ∣ x ∣

Add a constant to the solution

= 3 x + ln ∣ x ∣ + C

Popular Examples

integral of (2x^2-1)/((x-1)(x^2+2))

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

integral of 5x(x^2+8)^2

\int 5 x (x^{2} + 8)^{2} d x

integral of (e^{ln(x)})/(x^2+7)

\int \frac{e ^{l n (x)}}{x ^{2} + 7} d x

integral of 2x^{2/3}(1+3/2 x^{5/6})

\int 2 x^{\frac{2}{3}} (1 + \frac{3}{2} x^{\frac{5}{6}}) d x

integral of 5^{8x+3}

\int 5^{8 x + 3} d x

Frequently Asked Questions (FAQ)

What is the integral of 3+1/x ?
The integral of 3+1/x is 3x+ln|x|+C