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Popular >

integral of (x+3)/x

Solution

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

Solution

x + 3 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{x + 3}{x} : 1 + \frac{3}{x}

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

\int 1 d x = x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= x + 3 ln ∣ x ∣

Add a constant to the solution

= x + 3 ln ∣ x ∣ + C

Graph

Popular Examples

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\int - x^{2} + 2 x + 8 d x

integral of (20x^4+8)(2x^5+4x)^{15}

\int (20 x^{4} + 8) (2 x^{5} + 4 x)^{15} d x

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\int 80 x^{\frac{1}{2}} d x

integral of (cos(pi/(x^7)))/(x^8)

\int \frac{cos ( \frac{π}{x ^{7}} )}{x ^{8}} d x

integral of-cos(x)e^x

\int - cos (x) e^{x} d x

Frequently Asked Questions (FAQ)

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