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Popular >

integral of 8+1/x

Solution

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

Solution

8 x + ln ∣ x ∣ + C

Solution steps

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

\int 8 d x = 8 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 8 x + ln ∣ x ∣

Add a constant to the solution

= 8 x + ln ∣ x ∣ + C

Popular Examples

integral of (x^6)/((5-x^7)^2)

\int \frac{x ^{6}}{( 5 - x ^{7} ) ^{2}} d x

integral of x^3sqrt(x^2+10)

\int x^{3} x^{2} + 10 d x

integral of (x+4)/(x(x+2)^2)

\int \frac{x + 4}{x ( x + 2 ) ^{2}} d x

integral of 1/(sqrt(cosh(x)-sinh(x)))

\int \frac{1}{cosh ( x ) - sinh ( x )} d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of 8+1/x ?
The integral of 8+1/x is 8x+ln|x|+C