int (ln(x^2 + 9x +1) dx help solve
C Catherine New member Joined Sep 27, 2006 Messages 1 Sep 27, 2006 #1 int (ln(x^2 + 9x +1) dx help solve
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Sep 27, 2006 #2 Re: calculus Hello, Catherine! \(\displaystyle \L\int\)ln(x2 + 9x + 1) dx\displaystyle \ln(x^2\,+\,9x\,+\,1)\,dxln(x2+9x+1)dx Click to expand... Integrate it "by parts" . . . . . u = ln(x2 + 9x+1) dv = dx.du = 2x + 9x2 + 9x + 1 dx v = x\displaystyle \begin{array}{ccc}u\,=\,\ln(x^2\,+\,9x+1) & \;\;\; & dv\,= \,dx \\ . \\ du\,=\,\frac{2x\,+\,9}{x^2\,+\,9x\,+\,1}\,dx & \;\;\; & v\,=\,x\end{array}u=ln(x2+9x+1).du=x2+9x+12x+9dxdv=dxv=x We have: \(\displaystyle \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)x⋅2x + 9x2 + 9x + 1 dx\displaystyle x\cdot\frac{2x\,+\,9}{x^2\,+\,9x\,+\,1}\,dxx⋅x2+9x+12x+9dx . . . . . \(\displaystyle = \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)2x2 + 9xx2 + 9x + 1 dx\displaystyle \frac{2x^2\,+\,9x}{x^2\,+\,9x\,+\,1}\,dxx2+9x+12x2+9xdx . . . . . \(\displaystyle = \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)(2 − 9x + 2x2 + 9x + 1) dx\displaystyle \left(2\,-\,\frac{9x\,+\,2}{x^2\,+\,9x\,+\,1}\right)\,dx(2−x2+9x+19x+2)dx Can you finish it now/
Re: calculus Hello, Catherine! \(\displaystyle \L\int\)ln(x2 + 9x + 1) dx\displaystyle \ln(x^2\,+\,9x\,+\,1)\,dxln(x2+9x+1)dx Click to expand... Integrate it "by parts" . . . . . u = ln(x2 + 9x+1) dv = dx.du = 2x + 9x2 + 9x + 1 dx v = x\displaystyle \begin{array}{ccc}u\,=\,\ln(x^2\,+\,9x+1) & \;\;\; & dv\,= \,dx \\ . \\ du\,=\,\frac{2x\,+\,9}{x^2\,+\,9x\,+\,1}\,dx & \;\;\; & v\,=\,x\end{array}u=ln(x2+9x+1).du=x2+9x+12x+9dxdv=dxv=x We have: \(\displaystyle \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)x⋅2x + 9x2 + 9x + 1 dx\displaystyle x\cdot\frac{2x\,+\,9}{x^2\,+\,9x\,+\,1}\,dxx⋅x2+9x+12x+9dx . . . . . \(\displaystyle = \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)2x2 + 9xx2 + 9x + 1 dx\displaystyle \frac{2x^2\,+\,9x}{x^2\,+\,9x\,+\,1}\,dxx2+9x+12x2+9xdx . . . . . \(\displaystyle = \;x\cdot\ln(x^2\,+\,9x\,+\,1)\,-\,\L\int\)(2 − 9x + 2x2 + 9x + 1) dx\displaystyle \left(2\,-\,\frac{9x\,+\,2}{x^2\,+\,9x\,+\,1}\right)\,dx(2−x2+9x+19x+2)dx Can you finish it now/
