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Popular >

integral of (x+8)/x

Solution

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

Solution

x + 8 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

= x + 8 ln ∣ x ∣

Add a constant to the solution

= x + 8 ln ∣ x ∣ + C

Popular Examples

integral of 1/((x+1)^4)

\int \frac{1}{( x + 1 ) ^{4}} d x

integral of sin^3(5x)

\int sin^{3} (5 x) d x

integral of 1/(x(x^2-4)^{3/2)}

\int \frac{1}{x ( x ^{2} - 4 ) ^{\frac{3}{2}}} d x

integral from 0 to 20 of sqrt(4+3x)

\int_{0}^{20} 4 + 3 x d x

y^{''}-3y^'-4y=-3,y(0)=0,y^'(0)=0

y^{^{''}} - 3 y^{^{'}} - 4 y = - 3, y (0) = 0, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

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