Find the integral $\int\frac{-12e^{\frac{-4t}{5}}}{5\left(1+3e^{\frac{-4t}{5}}\right)^2}dt$

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Learn how to solve differential calculus problems step by step online. Find the integral int((-12e^((-4t)/5))/(5(1+3e^((-4t)/5))^2))dt. Simplify the expression. Take the constant \frac{1}{5} out of the integral. Multiply the fraction and term in -12\cdot \left(\frac{1}{5}\right)\int\frac{1}{\left(1+3e^{\frac{-4t}{5}}\right)^2e^{\frac{4t}{5}}}dt. We can solve the integral \int\frac{1}{\left(1+3e^{\frac{-4t}{5}}\right)^2e^{\frac{4t}{5}}}dt by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 1+3e^{\frac{-4t}{5}} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.