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- Integrate by partial fractions
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Multiplying polynomials $3$ and $y^6-4y^{-3}$
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$\int\left(3y^6-12y^{-3}\right)\left(y^7+14y^{-2}-7\right)^6dy$
Learn how to solve equations problems step by step online. Find the integral int(3(y^6-4y^(-3))(y^7+14y^(-2)+-7)^6)dy. Multiplying polynomials 3 and y^6-4y^{-3}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. We can solve the integral \int\left(3y^6+\frac{-12}{y^{3}}\right)\left(y^7+\frac{14}{y^{2}}-7\right)^6dy 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 y^7+\frac{14}{y^{2}}-7 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dy in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.
