On this blog post, I will show another intelligent way to tackle the problem(Hard and Intriguing Indefinite Integral Problem ) that to compute the following indefinite integral:
[MATH]\int \dfrac{(3x^{10}+2x^8-2)\sqrt[4]{x^{10}+x^8+1}}{x^6} \,dx[/MATH]
If we rewrite the integrand such that we have:
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Showing posts with label substitution method. Show all posts
Putnam Definite Integral Hard Problem: Evaluate $\displaystyle\int_0^{\frac{\pi}{2}}\frac{dx}{1+(\tan x)^{\sqrt{2}}}$.
Another hard definite integral but it is not as bad as it looks. Let's first try the substitution method:
Attempt I:
We are given to evaluate:
[MATH]I=\int_0^{\pi/2}\frac{1}{1+\left(\tan(x)\right)^{\sqrt{2}}}\,dx[/MATH]
If we use the substitution:
[MATH]u=\frac{\pi}{2}-x[/MATH]
Attempt I:
We are given to evaluate:
[MATH]I=\int_0^{\pi/2}\frac{1}{1+\left(\tan(x)\right)^{\sqrt{2}}}\,dx[/MATH]
If we use the substitution:
[MATH]u=\frac{\pi}{2}-x[/MATH]
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