Contoh Soal 1 Materi Integral Tak Tentu Fungsi Aljabar

$\begin{array}{l}\\ 1.& {\displaystyle \int x^{2}dx=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle \frac{1}{3}{x}^3+C}\\ \text{b}.{\displaystyle \frac{1}{4}{x}^6+C}\\ \text{c}.{\displaystyle \frac{1}{3}{x}^6+C}\\ \text{d}.{\displaystyle \frac{1}{6}{x}^3+C}\\ \text{e}.{\displaystyle \frac{2}{3}{x}^3+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int x^{2}dx={\displaystyle \frac{x^{2+1}}{2+1}+C={\displaystyle \frac{1}{3}{x}^3+C}}}\end{array}$

$\begin{array}{l}\\ 2.& {\displaystyle \int x^{-2}dx=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle -2x^{-1}+C}\\ \text{b}.{\displaystyle -x^{-1}+C}\\ \text{c}.{\displaystyle -\frac{1}{2}{x}^{-2}+C}\\ \text{d}.{\displaystyle -\frac{1}{3}{x}^{-3}+C}\\ \text{e}.{\displaystyle -3x^{-3}+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int x^{-2}dx={\displaystyle \frac{x^{-2+1}}{-2+1}+C={\displaystyle \frac{1}{-1}{x}^{-1}+C=-x^{-1}+C}}}\end{array}$.

$\begin{array}{l}\\ 3.& {\displaystyle \int x^{{.}^{\frac{1}{3}}}dx=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle \frac{3}{4}{x}^{\frac{4}{3}}+C}\\ \text{b}.{\displaystyle x^{\frac{4}{3}}+C}\\ \text{c}.{\displaystyle \frac{3}{4}{x}^{\frac{2}{3}}+C}\\ \text{d}.{\displaystyle x^{-\frac{2}{3}}+C}\\ \text{e}.{\displaystyle \frac{3}{4}{x}^{-\frac{2}{3}}+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int x^{{.}^{\frac{1}{3}}}dx={\displaystyle \frac{x^{\frac{1}{3}+1}}{{\displaystyle \frac{1}{3}+1}}+C={\displaystyle \frac{1}{{\displaystyle \frac{4}{3}}}{x}^{{.}^{\frac{4}{3}}}+C={\displaystyle \frac{3}{4}{x}^{{.}^{\frac{4}{3}}}+C.}}}}\end{array}$.

$\begin{array}{l}\\ 4.& {\displaystyle \int \frac{1}{x^3}dx=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle -\frac{1}{2x^2}+C}\\ \text{b}.{\displaystyle -\frac{2}{x^2}+C}\\ \text{c}.{\displaystyle \frac{1}{3x^4}+C}\\ \text{d}.{\displaystyle \frac{3}{x^4}+C}\\ \text{e}.{\displaystyle -\frac{1}{4x^3}+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}& {\displaystyle \int \frac{1}{x^3}dx=\int x^{-3}dx}\\ & ={\displaystyle \frac{x^{-3+1}}{-3+1}+C=\frac{x^{-2}}{-2}+C=-\frac{1}{2x^2}+C}\end{array}\end{array}$.

$\begin{array}{l}\\ 5.& {\displaystyle \int \frac{1}{3}{x}^{3}dx=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle \frac{1}{3}{x}^4+C}\\ \text{b}.{\displaystyle \frac{1}{4}{x}^4+C}\\ \text{c}.{\displaystyle x^4+C}\\ \text{d}.{\displaystyle \frac{1}{12}{x}^4+C}\\ \text{e}.{\displaystyle \frac{4}{3}{x}^4+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int \frac{1}{3}{x}^{3}dx={\displaystyle \frac{1}{3}.\frac{x^{3+1}}{3+1}+C={\displaystyle \frac{1}{12}{x}^4+C}}}\end{array}$.