Question

The reduction formula for this or if it is possible to solve this integral further in terms of n?

score 106 · Answer 1 · 2021-06-17 16:59:53

106

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The reduction formula for this or if it is possible to solve this integral further in terms of n?

Published on 17 Jun 2021 - 16:59

score 108 · Answer 2 · 2021-08-07 23:45:29

108

Views

Proving that the reduction formula for $I_{m,n}=\int\frac{x^m}{(a^2-x^2)^n}dx$ is $I_{m,n}=a^2I_{m-2,n}-I_{m-2,n-1}$

Published on 07 Aug 2021 - 23:45

score 128 · Answer 3 · 2021-11-12 10:22:18

128

Views

Calculate the integral $\int_0^{\infty} x^{11} e^{-x^3}dx$

Published on 12 Nov 2021 - 10:22

score 137 · Answer 4 · 2021-11-29 03:04:37

137

Views

Reduction formula for $\int x\tan^n(x)$

Published on 29 Nov 2021 - 3:04

score 117 · Answer 5 · 2021-12-24 22:11:43

117

Views

Is this Lauricella $\text F_\text D$ to hypergeometric R, from DLMF, conversion formula correct?

Published on 24 Dec 2021 - 22:11

score 201 · Answer 6 · 2022-01-05 07:53:44

201

Views

How do we handle the integral $I_{4}=\int\left(\frac{\cos \theta}{1+\sin ^{2} \theta}\right)^{4} d \theta$?

Published on 05 Jan 2022 - 7:53

score 1.2k · Answer 7 · 2022-01-28 03:27:24

1.2k

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How to find exact value of integral $\int_{0}^{\infty} \frac{1}{\left(x^{4}-x^{2}+1\right)^{n}}dx$?

Published on 28 Jan 2022 - 3:27

score 156 · Answer 8 · 2022-03-02 03:37:50

156

Views

How to tackle the integral $\int_{0}^{\pi} \frac{3 \pi x^{2}-2 x^{3}}{(1+\sin x)^{n}}dx, \textrm{ where } n \in N $

Published on 02 Mar 2022 - 3:37

score 232 · Answer 9 · 2022-03-03 08:34:45

232

Views

How to evaluate $\int x^n e^{x} \cos x d x$ and $\int x^n e^{x} \sin x d x?$

Published on 03 Mar 2022 - 8:34

score 64 · Answer 10 · 2022-03-10 03:16:46

64

Views

How to make use of a reduction formula for the integral $I_n= \int \frac{d x}{\left(x^{k}+1\right)^{n}},$ where $k\geq 2 \textrm{ and }n\in N$?

Published on 10 Mar 2022 - 3:16

score 63 · Answer 11 · 2022-05-13 00:32:09

63

Views

What is the general techique to solve the following type of recursive integrals?

Published on 13 May 2022 - 0:32

score 84 · Answer 12 · 2022-05-16 12:15:22

84

Views

Quite challenge: how to solve this functional equation?

Published on 16 May 2022 - 12:15

score 177 · Answer 13 · 2022-08-29 10:59:15

177

Views

How many methods are there to find the closed form of $ \int_{0}^{\frac{\pi}{2}} \frac{d x}{(\sin x+\cos x)^{ n}}, \textrm{ where } n\in N $

Published on 29 Aug 2022 - 10:59

score 40 · Answer 14 · 2022-09-01 22:57:45

40

Views

I found a reduction formula for odd-order Chebyshev polynomials. Is it new? Are there other ones like it?

Published on 01 Sep 2022 - 22:57

score 139 · Answer 15 · 2022-09-09 23:37:45

139

Views

Mistake on the reduction formula for $\int_0^{\frac{\pi}{2}}\cos^{2n}{(x)}\,dx$

Published on 09 Sep 2022 - 23:37

List Question

The reduction formula for this or if it is possible to solve this integral further in terms of n?

Proving that the reduction formula for $I_{m,n}=\int\frac{x^m}{(a^2-x^2)^n}dx$ is $I_{m,n}=a^2I_{m-2,n}-I_{m-2,n-1}$

Calculate the integral $\int_0^{\infty} x^{11} e^{-x^3}dx$

Reduction formula for $\int x\tan^n(x)$

Is this Lauricella $\text F_\text D$ to hypergeometric R, from DLMF, conversion formula correct?

How do we handle the integral $I_{4}=\int\left(\frac{\cos \theta}{1+\sin ^{2} \theta}\right)^{4} d \theta$?

How to find exact value of integral $\int_{0}^{\infty} \frac{1}{\left(x^{4}-x^{2}+1\right)^{n}}dx$?

How to tackle the integral $\int_{0}^{\pi} \frac{3 \pi x^{2}-2 x^{3}}{(1+\sin x)^{n}}dx, \textrm{ where } n \in N $

How to evaluate $\int x^n e^{x} \cos x d x$ and $\int x^n e^{x} \sin x d x?$

How to make use of a reduction formula for the integral $I_n= \int \frac{d x}{\left(x^{k}+1\right)^{n}},$ where $k\geq 2 \textrm{ and }n\in N$?

What is the general techique to solve the following type of recursive integrals?

Quite challenge: how to solve this functional equation?

How many methods are there to find the closed form of $ \int_{0}^{\frac{\pi}{2}} \frac{d x}{(\sin x+\cos x)^{ n}}, \textrm{ where } n\in N $

I found a reduction formula for odd-order Chebyshev polynomials. Is it new? Are there other ones like it?

Mistake on the reduction formula for $\int_0^{\frac{\pi}{2}}\cos^{2n}{(x)}\,dx$

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