Question

timed problem
score: 4/10
$int 6x^{5} dx$
answer
$30x^{4}+c$
$x^{6}+c$
$36x^{6}+c$
$\frac{3}{2}x^{4}+c$
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Explanation:

Step1: Apply power rule for integration

Recall the power rule: $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for $n
eq -1$. For $\int 6x^5 dx$, first factor out the constant:
$6\int x^5 dx$

Step2: Compute the integral

Apply the power rule to $\int x^5 dx$ where $n=5$:
$6 \times \frac{x^{5+1}}{5+1} + C = 6 \times \frac{x^6}{6} + C$

Step3: Simplify the expression

Cancel the 6 in numerator and denominator:
$x^6 + C$

Answer:

$x^6 + C$ (Option B)