Let's integrate

Calculus Level 3

$\large \displaystyle \int \frac{x^2+1}{x^3+3x} \, dx$

If the value of above expression is in the form $\frac{1}{A} \ln | x^A+Ax | +C$ , find $A$ .

The answer is 3.

1 solution

Rishabh Jain
Feb 14, 2016

$\Large d(x^3+3x)=3(x^2+1)dx$ Hence integration simplifies to: $\Large \dfrac{1}{3} \int \dfrac{d(\color{#007fff}{x^3+3x})}{\color{#007fff}{x^3+3x}}$ $\Large =\dfrac{1}{\color{#D61F06}{3}}\ln(x^{\color{#D61F06}{3}}+\color{#D61F06}{3}x)+C$ Hence $\huge A=\boxed{3}$

Let's integrate

The answer is 3.

1 solution

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