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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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Simplify the expression
Learn how to solve integrals of exponential functions problems step by step online.
$-12\int\frac{1}{5\left(1+3e^{\frac{-4t}{5}}\right)^2e^{\frac{4t}{5}}}dt$
Learn how to solve integrals of exponential functions 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.
