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Exercise

$\int\:\frac{1}{y^2lny}dy$

Step-by-step Solution

1

Apply the formula: $\int\frac{1}{x^2\ln\left(x\right)}dx$$=Ei\left(-\ln\left(x\right)\right)+C$, where $x=y$

$Ei\left(-\ln\left|y\right|\right)$
2

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$Ei\left(-\ln\left|y\right|\right)+C_0$

Final answer to the exercise

$Ei\left(-\ln\left|y\right|\right)+C_0$

Try other ways to solve this exercise

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  • Integrate by partial fractions
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  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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Main Topic: Integrals involving Logarithmic Functions

They are those integrals where the function that we are integrating is composed only of combinations of logarithmic functions.

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