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The quotient of powers of same base ($\frac{e^{\left(2x+3\right)}}{e^{\left(1-x\right)}}$) can be rewritten as the base to the power of the difference of the exponents
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$\int e^{\left(2x+3-\left(1-x\right)\right)}dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int((e^(2x+3))/(e^(1-x)))dx. The quotient of powers of same base (\frac{e^{\left(2x+3\right)}}{e^{\left(1-x\right)}}) can be rewritten as the base to the power of the difference of the exponents. Solve the product -\left(1-x\right). Simplify the expression inside the integral. We can solve the integral \int e^{\left(2+3x\right)}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 2+3x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.