Solve for c
c=\frac{6x^{\frac{5}{3}}}{5}+3С
Solve for x
x=\frac{216^{\frac{4}{5}}\left(6С+5c\right)^{\frac{3}{5}}}{216}
Quiz
Integration
5 problems similar to:
3 \int x ^ { 2 / 3 } d x = \frac { 3 x ^ { 5 / 3 } } { 5 } + c
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15\int x^{\frac{2}{3}}\mathrm{d}x=3x^{\frac{5}{3}}+5c
Multiply both sides of the equation by 5.
3x^{\frac{5}{3}}+5c=15\int x^{\frac{2}{3}}\mathrm{d}x
Swap sides so that all variable terms are on the left hand side.
5c=15\int x^{\frac{2}{3}}\mathrm{d}x-3x^{\frac{5}{3}}
Subtract 3x^{\frac{5}{3}} from both sides.
5c=6x^{\frac{5}{3}}+15С
The equation is in standard form.
\frac{5c}{5}=\frac{6x^{\frac{5}{3}}+15С}{5}
Divide both sides by 5.
c=\frac{6x^{\frac{5}{3}}+15С}{5}
Dividing by 5 undoes the multiplication by 5.
c=\frac{6x^{\frac{5}{3}}}{5}+3С
Divide 6x^{\frac{5}{3}}+15С by 5.
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