Practicing Success
Practicing Success
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If $\int \frac{1}{x+x^5} d x=f(x)+C$, then the value of $\int \frac{x^4}{x+x^5} d x$ is |
$\log x-f(x)+C$ $f(x)+\log x+C$ $f(x)-\log x+C$ none of these |
$\log x-f(x)+C$ |
We have, $I =\int \frac{x^4}{x+x^5} d x$ $\Rightarrow I =\int \frac{\left(x^4+1\right)-1}{x+x^5} d x$ $\Rightarrow I =\int \frac{1}{x} d x-\int \frac{1}{x+x^5} d x=\log x-f(x)+C$ |
