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Calculus · Definite-Integrals

Integrate 1/(1 - t) from 0 to 0.999000

\int_{0}^{0.999} \frac{1}{1 - t}\, dt

Step by step

  1. \int_{0}^{0.999} \frac{1}{1 - t}\, dt

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. u = 1 - t,\quad du = -1\, dt

    Substitute u = 1 - t.

  3. \int \frac{1}{1 - t}\, dt = \int - \frac{1}{u}\, d_u

    Rewrite the integral in terms of u.

  4. \int - \frac{1}{u}\, d_u = -1 \int \frac{1}{u}\, d_u

    Pull the constant -1 out of the integral.

  5. \int \frac{1}{u}\, d_u = \log{\left(u \right)}

    ∫ 1/u du = ln|u|.

  6. = - \log{\left(1 - t \right)}

    Substitute back u = 1 - t.

  7. F(0.999) - F(0) = \left(6.90775528\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  8. = 6.90775528

    Simplify.

Reveal the answer
6.90775528