Contoh Soal 1 Materi Integral Tak Tentu Fungsi Aljabar

$\begin{array}{ll}\\ 1.&\displaystyle \int x^{2}\: dx=\: ....\\ &\begin{array}{ll}\\ \textrm{a}.\quad \color{red}\displaystyle \frac{1}{3}x^{3}+C\\ \textrm{b}.\quad \displaystyle \frac{1}{4}x^{6}+C\\ \textrm{c}.\quad \displaystyle \frac{1}{3}x^{6}+C\\ \textrm{d}.\quad \displaystyle \frac{1}{6}x^{3}+C\\ \textrm{e}.\quad \displaystyle \frac{2}{3}x^{3}+C\end{array}\\\\ &\textbf{Jawab}:\\ &\displaystyle \int x^{2}\: dx=\displaystyle \frac{x^{2+1}}{2+1}+C= \displaystyle \frac{1}{3}x^{3}+C \end{array}$

$\begin{array}{ll}\\ 2.&\displaystyle \int x^{-2}\: dx=\: ....\\ &\begin{array}{ll}\\ \textrm{a}.\quad \displaystyle -2x^{-1}+C\\ \textrm{b}.\quad \color{red}\displaystyle -x^{-1}+C\\ \textrm{c}.\quad \displaystyle -\frac{1}{2}x^{-2}+C\\ \textrm{d}.\quad \displaystyle -\frac{1}{3}x^{-3}+C\\ \textrm{e}.\quad \displaystyle -3x^{-3}+C\end{array}\\\\ &\textbf{Jawab}:\\ &\displaystyle \int x^{-2}\: dx=\displaystyle \frac{x^{-2+1}}{-2+1}+C= \displaystyle \frac{1}{-1}x^{-1}+C=-x^{-1}+C \end{array}$.

$\begin{array}{ll}\\ 3.&\displaystyle \int x^{.^{\frac{1}{3}}}\: dx=\: ....\\ &\begin{array}{ll}\\ \textrm{a}.\quad \color{red}\displaystyle \frac{3}{4}x^{\frac{4}{3}}+C\\ \textrm{b}.\quad \displaystyle x^{\frac{4}{3}}+C\\ \textrm{c}.\quad \displaystyle \frac{3}{4}x^{\frac{2}{3}}+C\\ \textrm{d}.\quad \displaystyle x^{-\frac{2}{3}}+C\\ \textrm{e}.\quad \displaystyle \frac{3}{4}x^{-\frac{2}{3}}+C\end{array}\\\\ &\textbf{Jawab}:\\ &\displaystyle \int x^{.^{\frac{1}{3}}}\: dx=\displaystyle \frac{x^{\frac{1}{3}+1}}{\displaystyle \frac{1}{3}+1}+C= \displaystyle \frac{1}{\displaystyle \frac{4}{3}}x^{.^{\frac{4}{3}}}+C=\displaystyle \frac{3}{4}x^{.^{\frac{4}{3}}}+C. \end{array}$.

$\begin{array}{ll}\\ 4.&\displaystyle \int \frac{1}{x^{3}}\: dx=\: ....\\ &\begin{array}{ll}\\ \textrm{a}.\quad \color{red}\displaystyle -\frac{1}{2x^{2}}+C\\ \textrm{b}.\quad \displaystyle -\frac{2}{x^{2}}+C\\ \textrm{c}.\quad \displaystyle \frac{1}{3x^{4}}+C\\ \textrm{d}.\quad \displaystyle \frac{3}{x^{4}}+C\\ \textrm{e}.\quad \displaystyle -\frac{1}{4x^{3}}+C\end{array}\\\\ &\textbf{Jawab}:\\ &\begin{aligned}&\displaystyle \int \frac{1}{x^{3}}\: dx=\int x^{-3}\: dx\\ &=\displaystyle \frac{x^{-3+1}}{-3+1}+C=\frac{x^{-2}}{-2}+C=-\frac{1}{2x^{2}}+C \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 5.&\displaystyle \int \frac{1}{3}x^{3}\: dx=\: ....\\ &\begin{array}{ll}\\ \textrm{a}.\quad \displaystyle \frac{1}{3}x^{4}+C\\ \textrm{b}.\quad \displaystyle \frac{1}{4}x^{4}+C\\ \textrm{c}.\quad \displaystyle x^{4}+C\\ \textrm{d}.\quad \color{red}\displaystyle \frac{1}{12}x^{4}+C\\ \textrm{e}.\quad \displaystyle \frac{4}{3}x^{4}+C\end{array}\\\\ &\textbf{Jawab}:\\ &\displaystyle \int \frac{1}{3}x^{3}\: dx=\displaystyle \frac{1}{3}.\frac{x^{3+1}}{3+1}+C= \displaystyle \frac{1}{12}x^{4}+C \end{array}$.