1.$\displaystyle \int ln(2x+1)dx$ 2.$\displaystyle \int e^{2x}sin3xdx$ 3$\displaystyle \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr$ I'm from Vietnam,I can't do it, help me !
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Originally Posted by butbi9x 1.$\displaystyle \int ln(2x+1)dx$ 2.$\displaystyle \int e^{2x}sin3xdx$ 3$\displaystyle \int \frac{r^{3}}{\sqrt{4+r^{2}}}dr$ I'm from Vietnam,I can't do it, help me ! Hi 1. You can integrate by parts $\displaystyle \int ln(2x+1)dx = x ln(2x+1) - \int \frac{2x}{2x+1}dx$ $\displaystyle \int ln(2x+1)dx = x ln(2x+1) - x + \frac{1}{2} ln(2x+1)$ 2. Twice by parts 3. By parts with $\displaystyle u'(r) = \frac{r}{\sqrt{4+r^{2}}}$ and v(r)=rē
One way to do the third one is to sub $\displaystyle u^2 = 4+r^2$ And just to add on running-gag's advice for number 2, you can treat the integral as the unknown and solve for it.
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