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We can solve the integral $\int\sqrt{t^6+5t}\left(6t^5+5\right)dt$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
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$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve definite integrals problems step by step online. Integrate the function (t^6+5t)^1/2(6t^5+5) from 0 to 1. We can solve the integral \int\sqrt{t^6+5t}\left(6t^5+5\right)dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.