Final Answer
$\ln\left(x\right)-\frac{1}{21}e^{-21x}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(x^{\left(-1\right)}+e^{\left(-21\cdot1\right)\cdot x}\right)dx$
Specify the solving method
1
Simplifying
$\int\left(x^{-1}+e^{-21x}\right)dx$
Learn how to solve integrals of exponential functions problems step by step online.
$\int\left(x^{-1}+e^{-21x}\right)dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x^(-1)+e^(-21*1x))dx. Simplifying. 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).
Final Answer
$\ln\left(x\right)-\frac{1}{21}e^{-21x}+C_0$