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

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

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integral of (-1)/t

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

x \to 1 + lim (x^{\frac{x}{1 - x}})

x^{2} \frac{d y}{d x} = y - x y, y (- 1) = - 4

\frac{π}{( 2 x ) ^{5}}

2 sin (x) cos (x)

2 x^{2} - 1