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

The integral of (3x+3)^6 is (729x^7)/7+729x^6+2187x^5+3645x^4+3645x^3+2187x^2+729x+C

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integral of (3x+3)^6

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

\frac{729 x ^{7}}{7} + 729 x^{6} + 2187 x^{5} + 3645 x^{4} + 3645 x^{3} + 2187 x^{2} + 729 x + C

Solution steps

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

Expand

(3 x + 3)^{6} : 729 x^{6} + 4374 x^{5} + 10935 x^{4} + 14580 x^{3} + 10935 x^{2} + 4374 x + 729

= \int 729 x^{6} + 4374 x^{5} + 10935 x^{4} + 14580 x^{3} + 10935 x^{2} + 4374 x + 729 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 729 x^{6} d x + \int 4374 x^{5} d x + \int 10935 x^{4} d x + \int 14580 x^{3} d x + \int 10935 x^{2} d x + \int 4374 x d x + \int 729 d x

\int 729 x^{6} d x = \frac{729 x ^{7}}{7}

\int 4374 x^{5} d x = 729 x^{6}

\int 10935 x^{4} d x = 2187 x^{5}

\int 14580 x^{3} d x = 3645 x^{4}

\int 10935 x^{2} d x = 3645 x^{3}

\int 4374 x d x = 2187 x^{2}

\int 729 d x = 729 x

= \frac{729 x ^{7}}{7} + 729 x^{6} + 2187 x^{5} + 3645 x^{4} + 3645 x^{3} + 2187 x^{2} + 729 x

Add a constant to the solution

= \frac{729 x ^{7}}{7} + 729 x^{6} + 2187 x^{5} + 3645 x^{4} + 3645 x^{3} + 2187 x^{2} + 729 x + C

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What is the integral of (3x+3)^6 ?
The integral of (3x+3)^6 is (729x^7)/7+729x^6+2187x^5+3645x^4+3645x^3+2187x^2+729x+C