What is the integral of 6x(x^5-1/6) ?

The integral of 6x(x^5-1/6) is 6(1/12 x^2(6x^5-1)-(5x^7)/(14))+C

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integral of 6x(x^5-1/6)

\int 6 x (x^{5} - \frac{1}{6}) d x

6 (\frac{1}{12} x^{2} (6 x^{5} - 1) - \frac{5 x ^{7}}{14}) + C

Solution steps

\int 6 x (x^{5} - \frac{1}{6}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int x (x^{5} - \frac{1}{6}) d x

Apply Integration By Parts

: \frac{1}{12} x^{2} (6 x^{5} - 1) - \int \frac{5 x ^{6}}{2} d x

= 6 (\frac{1}{12} x^{2} (6 x^{5} - 1) - \int \frac{5 x ^{6}}{2} d x)

\int \frac{5 x ^{6}}{2} d x = \frac{5 x ^{7}}{14}

= 6 (\frac{1}{12} x^{2} (6 x^{5} - 1) - \frac{5 x ^{7}}{14})

Add a constant to the solution

= 6 (\frac{1}{12} x^{2} (6 x^{5} - 1) - \frac{5 x ^{7}}{14}) + C

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y^{^{''}} - 4 y^{^{'}} = - 4 y

What is the integral of 6x(x^5-1/6) ?
The integral of 6x(x^5-1/6) is 6(1/12 x^2(6x^5-1)-(5x^7)/(14))+C