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** Step-by-step Solution **

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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- 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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Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

Learn how to solve integrals of exponential functions problems step by step online.

$\int\left(\frac{1}{x}+e^{-21x}\right)dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x^(-1)+e^(-21x))dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Expand the integral \int\left(\frac{1}{x}+e^{-21x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left|x\right|. The integral \int e^{-21x}dx results in: \frac{1}{-21}e^{-21x}.

** Final answer to the problem

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