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$\begingroup$

$$\int \frac{x+1}{5x+4}dx$$

$$\frac{1}{5}\int \frac{5(x+1)}{5x+4}dx=\frac{1}{5}\int \frac{5x+5}{5x+4}dx=\frac{1}{5}\int (\frac{5x+4}{5x+4}+\frac{1}{5x+4})dx=\frac{1}{5}\int (1+\frac{1}{5x+4})dx=\frac{1}{5} (x+\frac{1}{5}ln|{5x+4}|+C)=\frac{x}{5}+\frac{ln|5x+4|}{25}+C$$

Is that correct? is there another way to solve it?

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    Perfectly fine. – 2017-01-22
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    no other easy way? don't worry you are right :) – 2017-01-22
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    This is correct and probably about as short as possible. With practice you won't need as write down as many steps, they'll just get done in your head. – 2017-01-22

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