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Popular >

integral of (8+x)/x

Solution

\int \frac{8 + x}{x} d x

Solution

8 ln ∣ x ∣ + x + C

Solution steps

\int \frac{8 + x}{x} d x

Expand

\frac{8 + x}{x} : \frac{8}{x} + 1

= \int \frac{8}{x} + 1 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{8}{x} d x + \int 1 d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int 1 d x = x

= 8 ln ∣ x ∣ + x

Add a constant to the solution

= 8 ln ∣ x ∣ + x + C

Popular Examples

integral of (x^2-2x+3)/(x^2+4x+8)

\int \frac{x ^{2} - 2 x + 3}{x ^{2} + 4 x + 8} d x

integral of (x^5)/(x^6-8)

\int \frac{x ^{5}}{x ^{6} - 8} d x

integral of ln(sqrt(x^2+1))

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

integral of 1/(x^{1/2)+x^{1/4}}

\int \frac{1}{x ^{\frac{1}{2}} + x ^{\frac{1}{4}}} d x

integral of (sec^2(x))/((1+tan(x))^3)

\int \frac{sec ^{2} ( x )}{( 1 + tan ( x ) ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of (8+x)/x ?
The integral of (8+x)/x is 8ln|x|+x+C