Show that integration of $\int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx = \log \left| {{x^2} + 3x} \right| + C$ ~~~~~[NCERT Exemp. Q. 2,Page 163 ]

Let $I = \int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx$

Let's put ${x^2} + 3x = t$

$ \Rightarrow $$(2x + 3)dx = dt$

therefore,$I = \int {\frac{1}{t}} dt = \log |t| + C$

$ = \log \left| {\left( {{x^2} + 3x} \right)} \right| + C$

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