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Question Number 184346 by Matica last updated on 05/Jan/23

$$\int \frac{xdx}{a+bx}=?$$

Answered by SEKRET last updated on 05/Jan/23

$$\frac{1}{\mathbf{b}}\cdot \int \frac{\mathbf{bx}+\mathbf{a}-\mathbf{a}}{\mathbf{bx}+\mathbf{a}}\mathbf{dx}=$$$$\frac{1}{\mathbf{b}}\cdot \int 1-\mathbf{a}\cdot \frac{1}{\mathbf{bx}+\mathbf{a}}\mathbf{dx}=\frac{\mathbf{x}}{\mathbf{b}}-\frac{\mathbf{a}}{{\mathbf{b}}^2}\cdot \mathbf{ln}(\mathbf{bx}+\mathbf{a})+\mathbf{C}$$$$\mathbf{aswer}\frac{1}{{\mathbf{b}}^2}\cdot (\mathbf{bx}-\mathbf{a}\cdot \mathbf{ln}(\mathbf{bx}+\mathbf{a}))+\mathbf{C}$$$$$$

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