How do you integrate $\int (x^{2} {(x^{3} + 1)}^{3}) d x$ $int (x^2(x^3 + 1)^3)dx$ ?

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How do you integrate $\int (x^{2} {(x^{3} + 1)}^{3}) d x$ $int (x^2(x^3 + 1)^3)dx$ ?

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Answer 1 · 2015-10-11T05:37:10

If we expand the product $x^{2} \cdot {(x^{3} + 1)}^{3}$ $x^2*(x^3+1)^3$ we get

$x^{11} + 3 x^{8} + 3 x^{5} + x^{2}$ $x^11+3x^8+3x^5+x^2$

hence we have that

$\int x^{2} {(x^{3} + 1)}^{3} d x = \int (x^{11} + 3 x^{8} + 3 x^{5} + x^{2}) d x = \frac{x^{12}}{12} + 3 \cdot \frac{x^{9}}{9} + 3 \cdot \frac{x^{6}}{6} + \frac{x^{3}}{3} = \frac{x^{12}}{12} + \frac{x^{9}}{3} + \frac{x^{6}}{2} + \frac{x^{3}}{3} + c$ $int x^2(x^3+1)^3dx=int (x^11+3x^8+3x^5+x^2)dx=x^12/12+3*x^9/9+3*x^6/6+x^3/3=x^12/12+x^9/3+x^6/2+x^3/3+c$

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How do you integrate $\int (x^{2} {(x^{3} + 1)}^{3}) d x$ $int (x^2(x^3 + 1)^3)dx$ ?

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How do you integrate int (x^2(x^3 + 1)^3)dx∫(x2(x3+1)3)dxint (x^2(x^3 + 1)^3)dx?

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How do you integrate $\int (x^{2} {(x^{3} + 1)}^{3}) d x$ $int (x^2(x^3 + 1)^3)dx$ ?