$\int ( x + 6 ) ^ { 10 } d x = \frac { ( x + 6 ) ^ { 11 } } { 11 } + C$

Name: $\int ( x + 6 ) ^ { 10 } d x = \frac { ( x + 6 ) ^ { 11 } } { 11 } + C$
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Question

Quizplus · Accepted Answer

This is an application of the power rule for integration, which states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for any real number $n \neq -1$. Here, $n = 10$, so the integral of $(x + 6)^{10}$ with respect to $x$ is indeed $\frac{(x + 6)^{11}}{11} + C$.

∫(x+6)10dx=(x+6)1111+C\int ( x + 6 ) ^ { 10 } d x = \frac { ( x + 6 ) ^ { 11 } } { 11 } + C∫(x+6)10dx=11(x+6)11​+C

$\int ( x + 6 ) ^ { 10 } d x = \frac { ( x + 6 ) ^ { 11 } } { 11 } + C$