Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 14

Special Integrals
It is assumed in all cases that division by zero is excluded. Also, in the following, $u, v, w$ are functions of $x$; $a, b, p, q, n$ any constants, restricted if indicated; $e = 2.71828 \ldots$ is the natural base of logarithms; $\ln u$ denotes the natural logarithm of $u$ where it is assumed that $u > 0$ [in general, to extend formulas to cases where $u < 0$ as well, replace $\ln u$ with $\ln \left\vert{u}\right\vert$]; all angles are in radians; all constants of integration are omitted but implied.

Integrals Involving $\cosh a x$
=== Integrals Involving $\sinh a x$ and $\cosh a x$ ===

Still to be completed

 * $14.290$: Primitive of Reciprocal of Cube of Root of a x squared plus b x plus c The case for $a > 0$ is done, but the technique does not work for $a < 0$


 * $14.293$: Primitive of Reciprocal of x by Cube of Root of a x squared plus b x plus c Needs completing, or a different direction taken instead


 * $14.294$: Primitive of Reciprocal of x squared by Cube of Root of a x squared plus b x plus c Get it into the advertised format


 * $14.295$: Primitive of Half Integer Power of a x squared plus b x plus c This only takes on the case where $a > 0$. The case where $a < 0$ needs to be addressed.


 * $14.297$: Primitive of Reciprocal of Half Integer Power of a x squared plus b x plus c This only takes on the case where $a > 0$. The case where $a < 0$ needs to be addressed.


 * $14.308$: Primitive of Reciprocal of x squared by x cubed plus a cubed squared Going nowhere


 * $14.335$: Primitive of Power of x over Even Power of x plus Even Power of a


 * $14.336$: Primitive of Power of x over Even Power of x minus Even Power of a


 * $14.337$: Primitive of Power of x over Odd Power of x plus Odd Power of a


 * $14.338$: Primitive of Power of x over Odd Power of x minus Odd Power of a


 * $14.361$: Primitive of Reciprocal of square of p plus q by Sine of a x Anyone care to finish it off?


 * $14.363$: Primitive of Reciprocal of p squared minus square of q by Sine of a x


 * $14.391$: Primitive of Reciprocal of square of p plus q by Cosine of a x


 * $14.393$: Primitive of Reciprocal of p squared minus square of q by Cosine of a x


 * $14.421$: Primitive of Reciprocal of p by Sine of a x plus q by 1 plus Cosine of a x Where to go from here?


 * $14.422$: Primitive of Reciprocal of p by Sine of a x plus q by Cosine of a x plus Root of p squared plus q squared


 * $14.423$: Primitive of Reciprocal of p by Sine of a x plus q by Cosine of a x minus Root of p squared plus q squared


 * $14.474$: Primitive of Arcsine of x over a over x


 * $14.496$: Primitive of Arcsecant of x over a over x


 * $14.501$: Primitive of Arccosecant of x over a over x