hasil dari integral x akar 4x+1 dx

[tex]
\text{misalkan }u=4x+1\Leftrightarrow x=\frac{u-1}{4}\\
\text{selanjutnya } du=4dx\Leftrightarrow\frac{1}{4}du=dx\\
\text{sehingga diperoleh}\\
\int x\sqrt{4x+1}dx\\
=\int\frac{u-1}{4}\sqrt{u}\cdot\frac{1}{4}du\\
=\frac{1}{16}\int(u-1)\cdot u^{\frac{1}{2}}du\\
=\frac{1}{16}\int\left(u^{\frac{3}{2}}-u^{\frac{1}{2}}\right)du\\
=\frac{1}{16}\left(\frac{2}{5}u^{\frac{5}{2}}-\frac{2}{3}u^{\frac{3}{2}}\right)+C\\
[/tex]