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Popular >

integral of t/(2-t)

Solution

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

Solution

- 2 ln ∣ 2 - t ∣ - t + C

Solution steps

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

\frac{t}{2 - t} = \frac{2}{2 - t} - 1

= \int \frac{2}{2 - t} - 1 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{2 - t} d t - \int 1 d t

\int \frac{2}{2 - t} d t = - 2 ln ∣ 2 - t ∣

\int 1 d t = t

= - 2 ln ∣ 2 - t ∣ - t

Add a constant to the solution

= - 2 ln ∣ 2 - t ∣ - t + C

Popular Examples

integral of (sqrt(1-x^4))/(x^5)

\int \frac{1 - x ^{4}}{x ^{5}} d x

integral of (6x^4+x-3)/(2x^3+2x^2-12x)

\int \frac{6 x ^{4} + x - 3}{2 x ^{3} + 2 x ^{2} - 12 x} d x

integral of (7x^2)/((x^2+3)^2)

\int \frac{7 x ^{2}}{( x ^{2} + 3 ) ^{2}} d x

integral of (10)/(x^3-4x^2+8x)

\int \frac{10}{x ^{3} - 4 x ^{2} + 8 x} d x

integral of (x+2)sqrt(6-x)

\int (x + 2) 6 - x d x

Frequently Asked Questions (FAQ)

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