What is the integral of (a+bx+x^5) ?

The integral of (a+bx+x^5) is ax+(bx^2)/2+(x^6)/6+C

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integral of (a+bx+x^5)

\int (a + b x + x^{5}) d x

a x + \frac{b x ^{2}}{2} + \frac{x ^{6}}{6} + C

Solution steps

\int a + b x + x^{5} 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

= \int a d x + \int b x d x + \int x^{5} d x

\int a d x = a x

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

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

= a x + \frac{b x ^{2}}{2} + \frac{x ^{6}}{6}

Add a constant to the solution

= a x + \frac{b x ^{2}}{2} + \frac{x ^{6}}{6} + C

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What is the integral of (a+bx+x^5) ?
The integral of (a+bx+x^5) is ax+(bx^2)/2+(x^6)/6+C