timed problem\nscore: 0/10 current time: 1.3\n∫x³dx\nanswer\n3x² + c\n1/4x⁴ + c\n3x⁴ + c\n2x² + c

Explanation:

Step1: Apply power - rule for integration

The power - rule for integration is $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$, where $n\neq - 1$. Here $n = 3$.

Step2: Calculate the integral

Substitute $n = 3$ into the power - rule formula: $\int x^3dx=\frac{x^{3+1}}{3 + 1}+C=\frac{1}{4}x^4+C$.

Answer:

$\frac{1}{4}x^4+C$