Final Answer
$t-\frac{25}{12}\sqrt[25]{t^{12}}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(1-t^{-\frac{13}{25}}\right)dx$
Specify the solving method
1
Expand the integral $\int\left(1-t^{-\frac{13}{25}}\right)dt$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int1dt+\int-t^{-\frac{13}{25}}dt$
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$\int1dt+\int-t^{-\frac{13}{25}}dt$
Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(1-t^(-13/25))dt. Expand the integral \int\left(1-t^{-\frac{13}{25}}\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dt results in: t. The integral \int-t^{-\frac{13}{25}}dt results in: -\frac{25}{12}\sqrt[25]{t^{12}}. Gather the results of all integrals.
Final Answer
$t-\frac{25}{12}\sqrt[25]{t^{12}}+C_0$