What is the integral of 7x(x^6-1/7) ?

The integral of 7x(x^6-1/7) is 7(1/14 x^2(7x^6-1)-(3x^8)/8)+C

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integral of 7x(x^6-1/7)

\int 7 x (x^{6} - \frac{1}{7}) d x

7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8}) + C

Solution steps

\int 7 x (x^{6} - \frac{1}{7}) d x

Take the constant out:

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

= 7 \cdot \int x (x^{6} - \frac{1}{7}) d x

Apply Integration By Parts

: \frac{1}{14} x^{2} (7 x^{6} - 1) - \int 3 x^{7} d x

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \int 3 x^{7} d x)

\int 3 x^{7} d x = \frac{3 x ^{8}}{8}

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8})

Add a constant to the solution

= 7 (\frac{1}{14} x^{2} (7 x^{6} - 1) - \frac{3 x ^{8}}{8}) + C

\int x^{\frac{9}{2}} d x

(x - 3) \frac{d y}{d x} = 4 (x - 3)^{4} + y

\frac{\partial}{\partial y} (e^{y x^{2}})

\int \frac{70}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

x \to 1 + lim (\frac{x + 7}{x + 2})

What is the integral of 7x(x^6-1/7) ?
The integral of 7x(x^6-1/7) is 7(1/14 x^2(7x^6-1)-(3x^8)/8)+C