Solve I _ { k } I = ∫ 3x^4+3x^2+1/x^2+1 wrt x

$$I _ { k } I = \int \frac { 3 x ^ { 4 } + 3 x ^ { 2 } + 1 } { x ^ { 2 } + 1 } d x$$

Solve for I

$$\left\{\begin{matrix}I=\frac{\arctan(x)+x^{3}+С}{I_{k}}\text{, }&I_{k}\neq 0\\I\in \mathrm{R}\text{, }&С=-\arctan(x)-x^{3}\text{ and }I_{k}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$I_{k}I=\arctan(x)+x^{3}+С$$

Divide both sides by I_{k}.

$$\frac{I_{k}I}{I_{k}}=\frac{\arctan(x)+x^{3}+С}{I_{k}}$$

Dividing by I_{k} undoes the multiplication by I_{k}.

$$I=\frac{\arctan(x)+x^{3}+С}{I_{k}}$$

Solve for I_k

$$\left\{\begin{matrix}I_{k}=\frac{\arctan(x)+x^{3}+С}{I}\text{, }&I\neq 0\\I_{k}\in \mathrm{R}\text{, }&С=-\arctan(x)-x^{3}\text{ and }I=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$II_{k}=\arctan(x)+x^{3}+С$$

Divide both sides by I.

$$\frac{II_{k}}{I}=\frac{\arctan(x)+x^{3}+С}{I}$$

Dividing by I undoes the multiplication by I.

$$I_{k}=\frac{\arctan(x)+x^{3}+С}{I}$$