How do you integrate $\int {(x + 5)}^{6}$ $int (x+5)^6$ using substitution?

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Answer 1 · 2016-07-22T13:33:37

$\int {(x + 5)}^{6} d x = \frac{1}{7} {(x + 5)}^{7} + C$ $int (x+5)^6dx = 1/7(x+5)^7 + C$

Let $u = x + 5 \Rightarrow d u = d x$ $u = x+5 implies du = dx$

$\int u^{6} d u = \frac{u^{7}}{7} + C$ $int u^6du = u^7/7 + C$

$therefore int (x+5)^6dx = 1/7(x+5)^7 + C$

How do you integrate int (x+5)^6∫(x+5)6int (x+5)^6 using substitution?