Contoh Soal 3 Materi Integral Tak Tentu Fungsi Aljabar

 $\begin{array}{l}\\ 11.& {\displaystyle \int d\left(2x\right)=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle x+C}\\ \text{b}.{\displaystyle 2x+C}\\ \text{c}.{\displaystyle 3x+C}\\ \text{d}.{\displaystyle 4x+C}\\ \text{e}.{\displaystyle 5x+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int d\left(2x\right)=\int 2dx=2x+C.}\end{array}$.

$\begin{array}{l}\\ 12.& {\displaystyle \int 5d\left(2x\right)=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle 5+C}\\ \text{b}.{\displaystyle \frac{5}{2}x+C}\\ \text{c}.{\displaystyle 5x+C}\\ \text{d}.{\displaystyle 10x+C}\\ \text{e}.{\displaystyle 25x+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & {\displaystyle \int 5d\left(2x\right)=\int 5.2dx=\int 10dx=10x+C.}\end{array}$.

$\begin{array}{l}\\ 13.& {\displaystyle \int 6xd\left(3x\right)=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle 18x^2+C}\\ \text{b}.{\displaystyle 9x^2+C}\\ \text{c}.{\displaystyle 5x^2+C}\\ \text{d}.{\displaystyle 3x^2+C}\\ \text{e}.{\displaystyle 2x^2+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}& {\displaystyle \int 6xd\left(3x\right)=\int 6x.3dx=\int 18xdx}\\ & ={\displaystyle \frac{18x^2}{2}+C=9x^2+C}\end{array}\end{array}$.

$\begin{array}{l}\\ 14.& {\displaystyle \int (8x^3-2x)d(-2x)=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle -16x^4+4x^2+C}\\ \text{b}.{\displaystyle 16x^4-4x^2+C}\\ \text{c}.{\displaystyle -4x^4-2x^2+C}\\ \text{d}.{\displaystyle -4x^4+2x^2+C}\\ \text{e}.{\displaystyle 4x^4-2x^2+C}\end{array}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}& {\displaystyle \int (8x^3-2x)d(-2x)}\\ & =\int (8x^3-2x).(-2dx)\\ & =\int (-16x^3+4x)dx\\ & ={\displaystyle -\frac{16x^4}{4}+\frac{4x^2}{2}+C}\\ & ={\displaystyle -4x^4+2x^2+C}\end{array}\end{array}$.

$\begin{array}{l}\\ 15.& {\displaystyle \int (x+3)d(2x+6)=....}\\ & \begin{array}{l}\\ \text{a}.{\displaystyle 4x^2+24x+C}\\ \text{b}.{\displaystyle 2x^2+12x+C}\\ \text{c}.{\displaystyle x^2+6x+C}\\ \text{d}.{\displaystyle 4x^2+C}\\ \text{e}.{\displaystyle x^2+C}\end{array}\\ \\ & \text{Jawab}:\\ & \begin{array}{|cc|}\hline \text{Pertama}& \text{Kedua}\\ \begin{array}{rl}& {\displaystyle \int (x+3)d(2x+6)}\\ & ={\displaystyle \frac{1}{2}\int (2x+6)d(2x+6)}\\ & ={\displaystyle \frac{1}{2}\left[\frac{1}{2}{(2x+6)}^2\right]+C}\\ & ={\displaystyle \frac{1}{4}(4x^2+24x+36)+C}\\ & ={\displaystyle \frac{4x^2}{4}+\frac{24x}{4}+\frac{36}{4}+C}\\ & =x^2+6x+\underset{C}{\underbrace{9+C}}\\ & =x^2+6x+C\end{array}& \begin{array}{rl}& {\displaystyle \int (x+3)d(2x+6)}\\ & =\int (x+3).\left(2dx\right)\\ & =\int (2x+6)dx\\ & ={\displaystyle \frac{2x^2}{2}+6x+C}\\ & =x^2+6x+C\\ & \\ & \\ & \end{array}\\ \hline\end{array}\end{array}$ .