Solve 3 - ∫ x^4 wrt x=3x^3/5+c

$$3 - \int x ^ { 4 } d x = \frac { 3 x ^ { 3 } } { 5 } + c$$

Solve for c

$$c=-\frac{x^{5}}{5}-\frac{3x^{3}}{5}-С+3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$15-5\int x^{4}\mathrm{d}x=3x^{3}+5c$$

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

$$3x^{3}+5c=15-5\int x^{4}\mathrm{d}x$$

Subtract 3x^{3} from both sides.

$$5c=15-5\int x^{4}\mathrm{d}x-3x^{3}$$

The equation is in standard form.

$$5c=15-5С-3x^{3}-x^{5}$$

Divide both sides by 5.

$$\frac{5c}{5}=\frac{15-5С-3x^{3}-x^{5}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$c=\frac{15-5С-3x^{3}-x^{5}}{5}$$

Divide 15-x^{5}-5С-3x^{3} by 5.

$$c=-\frac{x^{5}}{5}-\frac{3x^{3}}{5}-С+3$$