∫ 0 13 d x ( 1 + 2 x ) 2 3 {\displaystyle \int _{0}^{13}{\frac {dx}{\sqrt[{3}]{(1+2x)^{2}}}}} = ∫ 0 13 1 2 3 t 2 d t {\displaystyle \int _{0}^{13}{\frac {1}{2^{3}{\sqrt {t^{2}}}}}dt} = 1 2 ∫ 0 13 1 t 2 3 d t {\displaystyle {\frac {1}{2}}\int _{0}^{13}{\frac {1}{\sqrt[{3}]{t^{2}}}}dt} = 1 2 ∫ 0 13 1 t 2 3 d t {\displaystyle {\frac {1}{2}}\int _{0}^{13}{\frac {1}{t^{\frac {2}{3}}}}dt} = 1 2 3 t 3 {\displaystyle {\frac {1}{2}}3{\sqrt[{3}]{t}}} = 1 2 3 1 + 2 x 3 {\displaystyle {\frac {1}{2}}3{\sqrt[{3}]{1+2x}}} = 3 2 1 + 2 x 3 {\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x}}} = 3 2 1 + 2 x 3 | 0 13 {\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x}}{\bigg |}_{0}^{13}} = 3 2 1 + 2 x ∗ 13 3 − 3 2 1 + 2 ∗ 0 3 {\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x*13}}-{\frac {3}{2}}{\sqrt[{3}]{1+2*0}}} <math\ =3</math>
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![{\displaystyle {\frac {1}{2}}3{\sqrt[{3}]{1+2x}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/20415fd42cdb3705a79026c6b206e0d8eae227e1)
![{\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/af311e7d8c3cf04c63a34118cdc43ae40922fd8a)
![{\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x}}{\bigg |}_{0}^{13}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a499de07f4b55f145653fc30d4d5ebc73aaa144d)
![{\displaystyle {\frac {3}{2}}{\sqrt[{3}]{1+2x*13}}-{\frac {3}{2}}{\sqrt[{3}]{1+2*0}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6b11b0f2aaf612f19578317fe0894d48b4ce3756)