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Popular >

integral of x/(x+8)

Solution

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

Solution

x + 8 - 8 ln ∣ x + 8 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{u - 8}{u} d u

= \int \frac{u - 8}{u} d u

Expand

\frac{u - 8}{u} : 1 - \frac{8}{u}

= \int 1 - \frac{8}{u} d u

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 u - \int \frac{8}{u} d u

\int 1 d u = u

\int \frac{8}{u} d u = 8 ln ∣ u ∣

= u - 8 ln ∣ u ∣

Substitute back

u = x + 8

= x + 8 - 8 ln ∣ x + 8 ∣

Add a constant to the solution

= x + 8 - 8 ln ∣ x + 8 ∣ + C

Popular Examples

integral of xsqrt(5x+4)

\int x 5 x + 4 d x

integral of e^{7x}sin(e^{7x})

\int e^{7 x} sin (e^{7 x}) d x

integral of 1/((sin(x)+cos(x)))

\int \frac{1}{( sin ( x ) + cos ( x ) )} d x

integral of (10)/((1+x)^2)

\int \frac{10}{( 1 + x ) ^{2}} d x

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

\int \frac{1}{x ^{2}} e^{- \frac{1}{x}} d x

Frequently Asked Questions (FAQ)

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