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# Evaluate : $\int\large\frac{x^2}{1+x^3}$$dx Can you answer this question? ## 1 Answer 0 votes Toolbox: • Method of substitution: • Given \int f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t). • Consider I=\int f(x)dx. Step 1: I=\int\large\frac{x^2}{1+x^3}$$dx$
Let $1+x^3=t$
On differentiating with respect to $x$
$3x^2dx=dt$
$x^2dx=\large\frac{dt}{3}$
$I=\int \large\frac{dt/3}{1+x^3}$
$\;\;=\large\frac{1}{3}\int \large\frac{dt}{t}$
Step 2:
On integrating we get,
$\large\frac{1}{3}$$\log \mid t\mid+c Substituting for t we get, I=\large\frac{1}{3}$$\log \mid 1+x^3\mid +c$