Question

$int x^{10}e^{x^{11}}mathrm{d}x=square$

Explanation:

Step1: Use substitution method

Let $u = x^{11}$, then $du=11x^{10}dx$, and $x^{10}dx=\frac{1}{11}du$.

Step2: Rewrite the integral

The original integral $\int x^{10}e^{x^{11}}dx$ becomes $\frac{1}{11}\int e^{u}du$.

Step3: Integrate $e^{u}$

We know that $\int e^{u}du = e^{u}+C$. So $\frac{1}{11}\int e^{u}du=\frac{1}{11}e^{u}+C$.

Step4: Substitute back $u = x^{11}$

We get $\frac{1}{11}e^{x^{11}}+C$.

Answer:

$\frac{1}{11}e^{x^{11}}+C$