Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.3 Trigonometric Substitutions, #51 · Calculus · Techniques of integration

For … why does the answer have different forms for … and…

For $\int d x / (x^{2} + 2 b x + c)$ why does the answer have different forms for $b^{2} > c$ and $b^{2} < c$ ? What is the answer if $b^{2} = c$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.3 Trigonometric Substitutions, #51

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