\int k d x = k x + C ( k
Solve for C
\left\{\begin{matrix}C=\frac{С}{k}\text{, }&k\neq 0\\C\in \mathrm{R}\text{, }&С=0\text{ and }k=0\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=\frac{С}{C}\text{, }&C\neq 0\\k\in \mathrm{R}\text{, }&С=0\text{ and }C=0\end{matrix}\right.
Share
Copied to clipboard
kx+Ck=\int k\mathrm{d}x
Swap sides so that all variable terms are on the left hand side.
Ck=\int k\mathrm{d}x-kx
Subtract kx from both sides.
kC=С
The equation is in standard form.
\frac{kC}{k}=\frac{С}{k}
Divide both sides by k.
C=\frac{С}{k}
Dividing by k undoes the multiplication by k.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}