Solve any maths problem

Step by step

1. \int_{0}^{\infty} \frac{1}{\left(t + 1\right)^{2}}\, dt

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

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

   Substitute u = t + 1.

3. \int \frac{1}{\left(t + 1\right)^{2}}\, dt = \int \frac{1}{u^{2}}\, d_u

   Rewrite the integral in terms of u.

4. \int \frac{1}{u^{2}}\, d_u = - \frac{1}{u}

   Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

5. = - \frac{1}{t + 1}

   Substitute back u = t + 1.

6. F(\infty) - F(0) = \left(0\right) - \left(-1\right)

   Fundamental theorem of calculus: plug in the limits.

7. = 1

   Simplify.