What is the integral of (-1)/t ?

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

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integral of (-1)/t

integral

\frac{- 1}{t}

- ln ∣ t ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= - ln ∣ t ∣

Add a constant to the solution

= - ln ∣ t ∣ + C

\frac{2 x}{e ^{x}}

x^{3} \cdot (e^{- x})^{2}

\frac{x ^{2}}{( x ^{3} + 1 ) ^{\frac{1}{2}}}

\frac{- 2}{e ^{x}}

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