Find the function of $\int {(x^{2} + 1)}^{3} d x$ $int(x^2+1)^3dx$ ?

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Find the function of $\int {(x^{2} + 1)}^{3} d x$ $int(x^2+1)^3dx$ ?

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Answer 1 · 2018-02-11T10:06:45

$\int {(x^{2} + 1)}^{3} d x = \frac{1}{7} x^{7} + \frac{3}{5} x^{5} + x^{3} + x + C$ $int (x^2+1)^3 dx = 1/7x^7+3/5x^5+x^3+x+C$

Explanation:

It's probably most straightforward to multiply out the polynomial before integrating it:

$\int {(x^{2} + 1)}^{3} d x = \int x^{6} + 3 x^{4} + 3 x^{2} + 1 d x$ $int (x^2+1)^3 dx = int x^6+3x^4+3x^2+1 dx$

$\int {(x^{2} + 1)}^{3} d x = \frac{1}{7} x^{7} + \frac{3}{5} x^{5} + x^{3} + x + C$ $color(white)(int (x^2+1)^3 dx) = 1/7x^7+3/5x^5+x^3+x+C$

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Find the function of $\int {(x^{2} + 1)}^{3} d x$ $int(x^2+1)^3dx$ ?

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Explanation:

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Find the function of $\int {(x^{2} + 1)}^{3} d x$ $int(x^2+1)^3dx$ ?