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Popular >

integral of t/(t-2)

Solution

\int \frac{t}{t - 2} d t

Solution

t - 2 + 2 ln ∣ t - 2 ∣ + C

Solution steps

\int \frac{t}{t - 2} d t

Apply u-substitution

: \int \frac{u + 2}{u} d u

= \int \frac{u + 2}{u} d u

Expand

\frac{u + 2}{u} : 1 + \frac{2}{u}

= \int 1 + \frac{2}{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{2}{u} d u

\int 1 d u = u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= u + 2 ln ∣ u ∣

Substitute back

u = t - 2

= t - 2 + 2 ln ∣ t - 2 ∣

Add a constant to the solution

= t - 2 + 2 ln ∣ t - 2 ∣ + C

Popular Examples

integral of 1/(x-c)

\int \frac{1}{x - c} d x

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

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

limit as x approaches 1-of 4x-5

x \to 1 - lim (4 x - 5)

derivative of 2/(3x)derivative of

\frac{2}{3 x}

integral of-(12)/(x^{13)}

\int - \frac{12}{x ^{13}} d x

Frequently Asked Questions (FAQ)

What is the integral of t/(t-2) ?
The integral of t/(t-2) is t-2+2ln|t-2|+C