Integration by Parts
Find the u and dv of the integral:
\int\frac{ln(x)}{x^2}dx
u = ln(x), dv = \frac{1}{x^2}dx
\int sec(x)dx
ln|sec(x) + tan(x)| + C
\int \frac{1}{\sqrt(100-x^2)}dx
\arcsin(\frac{x}{9})+C
Write the partial fraction decomposition.
\frac{1}{(x+8)^3(x^2+2)}
\frac{Ax+B}{x^2+2}+\frac{C}{x+8}+\frac{D}{(x+8)^2}+\frac{E}{(x+8)^3}
\int \arctan(x)dx
xarctan(x)-\ln|x^2+1|+C
\int sin^2(x)cos^5(x)dx
\frac{1}{3}sin^3x-\frac{2}{5}sin^5x+\frac{1}{7}sin^7x + C
\int\frac{1}{\sqrt(49+x^2)dx
\ln|\frac{\sqrt(49+x^2)}{7}+\frac{x}{7}|+C
Write the partial fraction decomposition and solve for A and B.
\frac{3x+11}{x^2-x-6}
\frac{A}{x-3}+\frac{B}{x+2}
A=4, B=-1
\int \xtan^2(x)dx
-\frac{1}{2}x^2 + xtan(x) + \ln|\cos(x)|+C
\int sec^3(x) dx
\frac{1}{2}(secxtanx+ln|secx+tanx|)+C
\int\frac{x^3}{\sqrt(x^2-9))dx
27(\frac{\sqrt(x^2-9)}{3})+9(\sqrt(x^2-9)/3)^3+C
Write the form of the partial fraction decomposition.
\frac{(x+3)}{x^2(x^4-1)(x^2+1)}
\frac{Ax+B}{x^2}+\frac{Cx+D}{x^2+1}+\frac{Ex+F}{(x^2+1)^2}+\frac{G}{x+1}+\frac{H}{x-1}
\int \sin^2(x)dx
\frac{1}{2}(-\sin(x)\cos(x)+x)+C
\int tan^7xsec^7xdx
\frac{1}{13}\sec^13(x)-\frac{3}{11}\sec^11(x)+\frac{1}{3}\sec^9(x)-\frac{1}{7}sec^7(x)+C
\int\frac{1}{\sqrt(x^2+2x)}dx
ln|(x+1)+\sqrt((x+1)^2-1)|+C
\int \frac{2x^2-x+4}{(x^2+4)(x-1)}dx
\frac{1}{2}\ln|x^2+4|+\ln|x-1|+C
\int ln(x)^2 dx
\xln(x)^2 - 2xln(x) + 2x + C
\int \frac{\cos^3x}{\sqrt(\sinx)}dx
2\sqrt(\sinx)-\frac{2}{5}sin^(\frac{5}{2})x+C
\int(x-2)^3\sqrt(5+4x-x^2)dx
\frac{1}{5}(9-(x-2)^2)^(\frac{5}{2})-3(9-(x-2)^2)^(\frac{3}{2})+C
\int \frac{x-11}{(x^2+4)(x-1)}dx
\ln|x^2+4|+\frac{3}{2}\arctan(\frac{x}{2})-2\ln|x-1|+C