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$\int e^{\frac{7}{2}x}\left(\mathrm{sinh}\left(\frac{1}{2}\right)x+\mathrm{cosh}\left(\frac{1}{2}\right)x\right)dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(7/2x)(sinh(1/2)x+cosh(1/2)x))dx. Simplifying. Simplify the expression inside the integral. The integral of a function times a constant (1.6487213) is equal to the constant times the integral of the function. We can solve the integral \int e^{\frac{7}{2}x}xdx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x).