What is the integral of 1n(x^2+2x+2) ?

The integral of 1n(x^2+2x+2) is n((x^3)/3+x^2+2x)+C

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integral of 1n(x^2+2x+2)

\int 1 n (x^{2} + 2 x + 2) d x

n (\frac{x ^{3}}{3} + x^{2} + 2 x) + C

Solution steps

\int 1 \cdot n (x^{2} + 2 x + 2) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 1 \cdot n \cdot \int x^{2} + 2 x + 2 d x

Simplify

= n \cdot \int x^{2} + 2 x + 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= n (\int x^{2} d x + \int 2 x d x + \int 2 d x)

\int x^{2} d x = \frac{x ^{3}}{3}

\int 2 x d x = x^{2}

\int 2 d x = 2 x

= n (\frac{x ^{3}}{3} + x^{2} + 2 x)

Add a constant to the solution

= n (\frac{x ^{3}}{3} + x^{2} + 2 x) + C

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What is the integral of 1n(x^2+2x+2) ?
The integral of 1n(x^2+2x+2) is n((x^3)/3+x^2+2x)+C