What is the integral of (2+x^7)^3x^6 ?

The integral of (2+x^7)^3x^6 is (8x^7)/7+(6x^{14})/7+(2x^{21})/7+(x^{28})/(28)+C

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integral of (2+x^7)^3x^6

\int (2 + x^{7})^{3} x^{6} d x

\frac{8 x ^{7}}{7} + \frac{6 x ^{14}}{7} + \frac{2 x ^{21}}{7} + \frac{x ^{28}}{28} + C

Solution steps

\int (2 + x^{7})^{3} x^{6} d x

Expand

(2 + x^{7})^{3} x^{6} : 8 x^{6} + 12 x^{13} + 6 x^{20} + x^{27}

= \int 8 x^{6} + 12 x^{13} + 6 x^{20} + x^{27} 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 8 x^{6} d x + \int 12 x^{13} d x + \int 6 x^{20} d x + \int x^{27} d x

\int 8 x^{6} d x = \frac{8 x ^{7}}{7}

\int 12 x^{13} d x = \frac{6 x ^{14}}{7}

\int 6 x^{20} d x = \frac{2 x ^{21}}{7}

\int x^{27} d x = \frac{x ^{28}}{28}

= \frac{8 x ^{7}}{7} + \frac{6 x ^{14}}{7} + \frac{2 x ^{21}}{7} + \frac{x ^{28}}{28}

Add a constant to the solution

= \frac{8 x ^{7}}{7} + \frac{6 x ^{14}}{7} + \frac{2 x ^{21}}{7} + \frac{x ^{28}}{28} + C

f (x) = 3 x^{3}

\int 6 x d x

y = \frac{x ^{2} + 9}{( 7 x - 1 ) ^{5}}

\frac{x ^{2}}{( 6 + x ) ^{5}}

n = 1 \sum \infty \frac{2 n}{5 n - 6}

What is the integral of (2+x^7)^3x^6 ?
The integral of (2+x^7)^3x^6 is (8x^7)/7+(6x^{14})/7+(2x^{21})/7+(x^{28})/(28)+C