Porisma

A hint to get started

Complete the square before choosing a form

Find (a) ∫1t2+4t+13 dt\int\frac1{t^2+4t+13}\,dt; (b) ∫12x2+8x+9 dx\int\frac1{2x^2+8x+9}\,dx; (c) ∫113+8x−4x2 dx\int\frac1{\sqrt{13+8x-4x^2}}\,dx.

CJC · Lecture · Example 6

Normalise the squared-variable coefficient to 1 before completing the square.

The Teacher highlights completing the square and comparing coefficients in (x+a) squared plus b; the f/f-prime scaffolds use shifts with derivative 1.

Read the worked solution