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Popular >

integral of (1-t)/t

Solution

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

Solution

ln ∣ t ∣ - t + C

Solution steps

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

Expand

\frac{1 - t}{t} : \frac{1}{t} - 1

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

\int \frac{1}{t} d t = ln ∣ t ∣

\int 1 d t = t

= ln ∣ t ∣ - t

Add a constant to the solution

= ln ∣ t ∣ - t + C

Popular Examples

limit as x approaches 1 of 3x^3-5x^2+x+5

x \to 1 lim (3 x^{3} - 5 x^{2} + x + 5)

derivative of-1/5 cos(5x)

\frac{d}{d x} (- \frac{1}{5} cos (5 x))

y^{''}-6y^'+13y=0,y(0)=0,y^'(0)=-3

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

y y^{^{'}} - 6 e^{x} = 0

derivative of \sqrt[3]{sin^2(2x})

Frequently Asked Questions (FAQ)

What is the integral of (1-t)/t ?
The integral of (1-t)/t is ln|t|-t+C