What is the integral of (x^6+2x^5+3x^4) ?

The integral of (x^6+2x^5+3x^4) is (x^7)/7+(x^6)/3+(3x^5)/5+C

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integral of (x^6+2x^5+3x^4)

\int (x^{6} + 2 x^{5} + 3 x^{4}) d x

\frac{x ^{7}}{7} + \frac{x ^{6}}{3} + \frac{3 x ^{5}}{5} + C

Solution steps

\int x^{6} + 2 x^{5} + 3 x^{4} 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 x^{6} d x + \int 2 x^{5} d x + \int 3 x^{4} d x

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

= \frac{x ^{7}}{7} + \frac{x ^{6}}{3} + \frac{3 x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{x ^{6}}{3} + \frac{3 x ^{5}}{5} + C

What is the integral of (x^6+2x^5+3x^4) ?
The integral of (x^6+2x^5+3x^4) is (x^7)/7+(x^6)/3+(3x^5)/5+C