Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.3 Trigonometric Substitutions, #42 · Calculus · Techniques of integration

Rewrite 43–48 as … or … by completing the square

Substitute $x = sin θ$ , $cos θ$ , or $tanh θ$ . After integration change back to $x$ .

$\int \frac{1 + x ^{2}}{x ^{2}} d x$

Rewrite 43–48 as $(x + b)^{2} + C$ or $- (x - b)^{2} + C$ by completing the square.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.3 Trigonometric Substitutions, #42

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