What is the integral of (3x-sqrt(2))^5 ?

The integral of (3x-sqrt(2))^5 is (81x^6)/2-81sqrt(2)x^5+135x^4-60sqrt(2)x^3+30x^2-4sqrt(2)x+C

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integral of (3x-sqrt(2))^5

\int (3 x - 2)^{5} d x

\frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x + C

Solution steps

\int (3 x - 2)^{5} d x

Expand

(3 x - 2)^{5} : 243 x^{5} - 4052 x^{4} + 540 x^{3} - 90 \cdot 2^{\frac{3}{2}} x^{2} + 60 x - 2^{\frac{5}{2}}

= \int 243 x^{5} - 4052 x^{4} + 540 x^{3} - 90 \cdot 2^{\frac{3}{2}} x^{2} + 60 x - 2^{\frac{5}{2}} 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 243 x^{5} d x - \int 4052 x^{4} d x + \int 540 x^{3} d x - \int 90 \cdot 2^{\frac{3}{2}} x^{2} d x + \int 60 x d x - \int 2^{\frac{5}{2}} d x

\int 243 x^{5} d x = \frac{81 x ^{6}}{2}

\int 4052 x^{4} d x = 812 x^{5}

\int 540 x^{3} d x = 135 x^{4}

\int 90 \cdot 2^{\frac{3}{2}} x^{2} d x = 602 x^{3}

\int 60 x d x = 30 x^{2}

\int 2^{\frac{5}{2}} d x = 42 x

= \frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x

Add a constant to the solution

= \frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x + C

What is the integral of (3x-sqrt(2))^5 ?
The integral of (3x-sqrt(2))^5 is (81x^6)/2-81sqrt(2)x^5+135x^4-60sqrt(2)x^3+30x^2-4sqrt(2)x+C