What is the integral of (ax^6+bx^4+3c) ?

The integral of (ax^6+bx^4+3c) is (ax^7)/7+(bx^5)/5+3cx+C

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integral of (ax^6+bx^4+3c)

\int (a x^{6} + b x^{4} + 3 c) d x

\frac{a x ^{7}}{7} + \frac{b x ^{5}}{5} + 3 c x + C

Solution steps

\int a x^{6} + b x^{4} + 3 c 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 x^{6} d x + \int b x^{4} d x + \int 3 c d x

\int a x^{6} d x = \frac{a x ^{7}}{7}

\int b x^{4} d x = \frac{b x ^{5}}{5}

\int 3 c d x = 3 c x

= \frac{a x ^{7}}{7} + \frac{b x ^{5}}{5} + 3 c x

Add a constant to the solution

= \frac{a x ^{7}}{7} + \frac{b x ^{5}}{5} + 3 c x + C

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What is the integral of (ax^6+bx^4+3c) ?
The integral of (ax^6+bx^4+3c) is (ax^7)/7+(bx^5)/5+3cx+C