Nilai \int_{-1}^{0}x\sqrt{x+1}\ dx=⋯
Misalkan u^2=x+1 dan 2udu=dx. Tulis ulang integral taktentu dalam variable u.
\begin{align*}\int x\sqrt{x+1}\, dx &=\int (u^2-1)\cdot u\cdot 2u\, du\\ &=\int 2u^4-2u^2\,du\\ &=\frac{2}{5}u^5-\frac{2}{3}u^3+C\\ &=\frac{2}{5}(x+1)^{5/2}-\frac{2}{3}(x+1)^{3/2}+C\end{align*}
Dengan demikian \displaystyle \int_{-1}^0 x\sqrt{x+1}=\biggl[ \frac{2}{5}(x+1)^{5/2}-\frac{2}{3}(x+1)^{3/2} \biggr]_{-1}^0=\frac{2}{5}-\frac{2}{3}=-\frac{4}{15}.
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