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

\frac{1}{( s ^{2} + 5 )}

f (x) = \frac{1 - 4 x}{1 + 4 x}

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 2)

x d y - y d x = (x y)^{\frac{1}{2}}

\frac{\partial}{\partial x} (6 e^{x^{5} y})

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