Calculate the integral below. ∫e−5xarctan(e5x)dx First, perform partial integration: ∫udv=uv−∫vdu Here; u=? and dv=h(x)dx where h(x) =? should be Note: use arctan(x) for the inverse trigonometric function tan−1(x). Thus, the integral obtained on the right is ∫vdu=∫f(x)dx. f(x)=? Calculating this integral and substituting it in the partial integration formula, we get the result as follows: ∫e−5xarctan(e5x)dx=?
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 this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
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.
Calculate the integral below.
∫e−5xarctan(e5x)dx
First, perform partial
∫udv=uv−∫vdu
Here;
u=?
and dv=h(x)dx where h(x) =? should be
Note: use arctan(x) for the inverse trigonometric function tan−1(x).
Thus, the integral obtained on the right is ∫vdu=∫f(x)dx.
f(x)=?
Calculating this integral and substituting it in the partial integration formula, we get the result as follows:
∫e−5xarctan(e5x)dx=?
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