Final Answer
Step-by-step Solution
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We could not solve this problem by using the method: Integrate by trigonometric substitution
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. We can solve the integral \int e^{-21x}dx 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 -21x 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 dx 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.