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Popular >

integral of x/(x-7)

Solution

\int \frac{x}{x - 7} d x

Solution

x - 7 + 7 ln ∣ x - 7 ∣ + C

Solution steps

\int \frac{x}{x - 7} d x

Apply u-substitution

: \int \frac{u + 7}{u} d u

= \int \frac{u + 7}{u} d u

Expand

\frac{u + 7}{u} : 1 + \frac{7}{u}

= \int 1 + \frac{7}{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{7}{u} d u

\int 1 d u = u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

= u + 7 ln ∣ u ∣

Substitute back

u = x - 7

= x - 7 + 7 ln ∣ x - 7 ∣

Add a constant to the solution

= x - 7 + 7 ln ∣ x - 7 ∣ + C

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\int 5 sin (6 π) t d t

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\frac{2 x}{x ^{2} + 1}

x^{''}+3x^'+2x=e^{-t}

x^{^{''}} + 3 x^{^{'}} + 2 x = e^{- t}

tangent of sqrt((3x+25))tangent of

(3 x + 25)

Frequently Asked Questions (FAQ)

What is the integral of x/(x-7) ?
The integral of x/(x-7) is x-7+7ln|x-7|+C