Evaluate the following indefinite integral.
$\int (11 x^{10} - \frac{10}{x^{10}}) d x$
$\int (11 x^{10} - \frac{10}{x^{10}}) d x = ◻$

Answer

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Answer

So, the solution to the integral $\int (11 x^{10} - \frac{10}{x^{10}}) d x$ is $x^{11} + \frac{10}{9 x^{9}}$

Steps

Step 1 ：Given the integral $\int (11 x^{10} - \frac{10}{x^{10}}) d x$

Step 2 ：We can split this integral into two parts: $\int 11 x^{10} d x$ and $\int - \frac{10}{x^{10}} d x$

Step 3 ：The integral of $11 x^{10}$ with respect to $x$ is $\frac{1}{10 + 1} \cdot 11 \cdot x^{10 + 1} = x^{11}$

Step 4 ：The integral of $- \frac{10}{x^{10}}$ with respect to $x$ is $- \frac{1}{10 - 1} \cdot - 10 \cdot x^{1 - 10} = \frac{10}{9 x^{9}}$

Step 5 ：Adding these two integrals together, we get $x^{11} + \frac{10}{9 x^{9}}$

Step 6 ：So, the solution to the integral $\int (11 x^{10} - \frac{10}{x^{10}}) d x$ is $x^{11} + \frac{10}{9 x^{9}}$