How do you integrate $\int x {(3 x + 1)}^{10}$ $int x (3x+1)^10$ ?

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Answer 1 · 2015-11-02T20:34:24

Use substitution with $u = 3 x + 1$ $u = 3x+1$

$\int x {(3 x + 1)}^{10} d x$ $int x (3x+1)^10 dx$

Let $u = 3 x + 1$ $u = 3x+1$ , so that $d u = 3 d x$ $du = 3dx$ and $x = \frac{1}{3} (u - 1)$ $x = 1/3(u-1)$

The integral becomes:

$\int \frac{1}{3} (u - 1) u^{10} \frac{1}{3} d u = \frac{1}{9} \int (u^{11} - u^{10}) d u$ $int 1/3(u-1) u^10 1/3 du = 1/9 int (u^11-u^10) du$

The student is encouraged to finish from here.

How do you integrate int x (3x+1)^10 ∫x(3x+1)10int x (3x+1)^10 ?