What is the integral of 3(x^5-x^3+1) ?

The integral of 3(x^5-x^3+1) is 3((x^6)/6-(x^4)/4+x)+C

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integral of 3(x^5-x^3+1)

\int 3 (x^{5} - x^{3} + 1) d x

3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x) + C

Solution steps

\int 3 (x^{5} - x^{3} + 1) d x

Take the constant out:

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

= 3 \cdot \int x^{5} - x^{3} + 1 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

= 3 (\int x^{5} d x - \int x^{3} d x + \int 1 d x)

\int x^{5} d x = \frac{x ^{6}}{6}

\int x^{3} d x = \frac{x ^{4}}{4}

\int 1 d x = x

= 3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x)

Add a constant to the solution

= 3 (\frac{x ^{6}}{6} - \frac{x ^{4}}{4} + x) + C

What is the integral of 3(x^5-x^3+1) ?
The integral of 3(x^5-x^3+1) is 3((x^6)/6-(x^4)/4+x)+C