| xmdx | dx | xmdx | ||
| √1-x2 | , | xm √1-x2 | , | √ax-x |
Integration of the differentials
F(log x) dx x , F sin-1x dx √1-x2 , x(log xn)dx, xm eax dx, (sin-1xm)dx.
Integration of the differentials eax sin bxdx and eax cos bxdx.
Integration of (sin xm.)(cos xn) dx.
Integration by series. Application to the expression
| dx |
| √ax-x2 √1-bx |
Application of integration by series to the development of functions, the development of whose derivatives is given: tan-1x, sin-1x, log(1 + x.)
Lessons 35–38. Geometrical Applications.
Quadrature of certain curves. Circle, hyperbola, cycloid, logarithmic spiral, &c.