Интегралы содержащие a+bx

\[ \int \frac{dx}{a+bx} = \frac{1}{b}\ln(a+bx)+C \]

\[ \int (a+bx)^n dx = \frac{(a+bx)^{n+1}}{b(n+1)}+C \]

\[ \int \frac{x dx}{a+bx} = \frac{1}{b^2}[a+bx-a·\ln(a+bx)]+C \]

\[ \int \frac{x^2 dx}{a+bx} = \\ = \frac{1}{b^2}[\frac{1}{2}(a+bx)^2-2a·(a+bx)+a^2·\ln(a+bx)]+C \]

\[ \int \frac{dx}{x(a+bx)} = -\frac{1}{a}\ln(\frac{a+bx}{x})+C \]

\[ \int \frac{dx}{x^2(a+bx)} = -\frac{1}{ax}+\frac{b}{a^2}\ln(\frac{a+bx}{x})+C \]

\[ \int \frac{x dx}{(a+bx)^2} = \frac{1}{b^2}[\ln(a+bx)+\frac{a}{a+bx}]+C \]

\[ \int \frac{x^2 dx}{(a+bx)^2} = \\ = \frac{1}{b^3}[a+bx-2a·\ln(a+bx)-\frac{a^2}{a+bx}]+C \]

\[ \int \frac{dx}{x(a+bx)^2} = \frac{1}{a(a+bx)}-\frac{1}{a^2}\ln(\frac{a+bx}{x})+C \]

\[ \int \frac{x dx}{(a+bx)^3} = \frac{1}{b^2}[-\frac{1}{a+bx}+\frac{a}{2(a+bx)^2}]+C \]