x 2 + 3x dx = | x 2 + 3x | + C

Let I = x 2 + 3x dx Let's put x 2 + 3x = t (2x + 3)dx = dt therefore, I = t dt = |t| + C = | ( x 2 + 3x ) | + C Evaluate the following :

class 12 maths integrals

$\int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx = \log \left| {{x^2} + 3x} \right| + C$

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📘 Integrals NCERT Exemp. Q. 2,Page 163 SA

$\int {\frac{{2x + 3}}{{{x^2} + 3x}}} dx = \log \left| {{x^2} + 3x} \right| + C$

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

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

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

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

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

Evaluate the following :

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