Solve ∫ left(7x-2right) wrt x=left(7x-2right)^4/28+c

$$\int{ \left( 7x-2 \right) }d x = \frac{ { \left(7x-2 \right) }^{ 4 } }{ 28 } +c$$

Solve for c

$$c=-\frac{\left(7x-2\right)^{4}}{28}+\frac{7x^{2}}{2}-2x+С$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28.

$$28\int 7x-2\mathrm{d}x=\left(7x-2\right)^{4}+28c$$

Swap sides so that all variable terms are on the left hand side.

$$\left(7x-2\right)^{4}+28c=28\int 7x-2\mathrm{d}x$$

Subtract \left(7x-2\right)^{4} from both sides.

$$28c=28\int 7x-2\mathrm{d}x-\left(7x-2\right)^{4}$$

The equation is in standard form.

$$28c=-\left(7x-2\right)^{4}+98x^{2}+28С-56x$$

Divide both sides by 28.

$$\frac{28c}{28}=\frac{-\left(7x-2\right)^{4}+98x^{2}+28С-56x}{28}$$

Dividing by 28 undoes the multiplication by 28.

$$c=\frac{-\left(7x-2\right)^{4}+98x^{2}+28С-56x}{28}$$

Divide 98x^{2}-56x+28С-\left(7x-2\right)^{4} by 28.

$$c=-\frac{\left(7x-2\right)^{4}}{28}+\frac{7x^{2}}{2}-2x+С$$