Explanation ∫ e x e 2 x − 1 d x Usingintegration by parts u = e 2 x − 1 ; v ' = e x Now, integrating the given equation ∫ e x e 2 x − 1 d x = e 2 x − 1 . e x − ∫ e 2 x . e x e 2 x − 1 d x = e 2 x − 1 . e x − ∫ e 3 x e 2 x − 1 d x Considering the second term, i.e. the integral part ∫ e 3 x e 2 x − 1 d x Using substitution, u = e 2 x − 1 ∫ e 3 x e 2 x − 1 d x = ∫ u + 1 2 u d u = 1 2 ∫ u + 1 u d u Now using integration by parts u = u + 1 u ; v ' = 1 = 1 2 [ u + 1 u

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Chapter 8.6, Problem 50E

To determine

To evaluate the integral, $\int e^{x} \sqrt{e^{2 x} - 1} d x$ .

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Chapter 8.6, Problem 49E

Chapter 8.6, Problem 51E

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Chapter 8 Solutions

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To evaluate the integral, ∫ e x e 2 x − 1 d x .

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To evaluate the integral, $\int e^{x} \sqrt{e^{2 x} - 1} d x$ .

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To evaluate the integral, ∫ e x e 2 x − 1 d x .

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