Solve ∫ e^ln(1-t)/1-tdt

$$\int \frac { e ^ { \ln ( 1 - t ) } } { 1 - t } d t$$

Evaluate

$$t+С$$

Solution Steps

Apply rule a^{\log_{a}\left(b\right)}=b, where a=e and b=1-t.

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

Cancel out -t+1 in both numerator and denominator.

$$\int 1\mathrm{d}t$$

Find the integral of 1 using the table of common integrals rule \int a\mathrm{d}t=at.

$$t$$

If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$t+С$$

Differentiate w.r.t. t

$$1$$