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by jacks
Thu May 24, 2018 6:46 am
Forum: Analysis
Topic: Trigonometric Integration
Replies: 0
Views: 338

Trigonometric Integration

Finding $$\int\frac{1}{(\sin x+a\sec x)^2}dx$$
by jacks
Thu May 24, 2018 6:44 am
Forum: Analysis
Topic: Logrithmic Integral
Replies: 3
Views: 602

Re: Logrithmic Integral

Thanks kostakos and Riemann
by jacks
Sat May 12, 2018 11:23 am
Forum: Analysis
Topic: Logarithmic and Trigonometric Integral
Replies: 2
Views: 398

Re: Logarithmic and Trigonometric Integral

Thanks Riemann answer is Right. would you like to explain me in detail.
by jacks
Sat May 12, 2018 7:36 am
Forum: Analysis
Topic: Logarithmic and Trigonometric Integral
Replies: 2
Views: 398

Logarithmic and Trigonometric Integral

$$\int^{\frac{\pi}{6}}_{0}\ln^2(2\sin x)dx$$
by jacks
Sat May 12, 2018 7:35 am
Forum: Analysis
Topic: Logrithmic Integral
Replies: 3
Views: 602

Logrithmic Integral

$$\int^{\pi}_{0}x^2\ln(\sin x)dx$$
by jacks
Thu Jul 14, 2016 1:05 pm
Forum: Calculus
Topic: Integration using Substitution
Replies: 1
Views: 488

Integration using Substitution

Calculation of \(\displaystyle \int \frac{5x^3+3x-1}{(x^3+3x+1)^3}dx\)
by jacks
Thu Jul 14, 2016 10:24 am
Forum: Calculus
Topic: Definite integral
Replies: 3
Views: 767

Definite integral

Evaluation of definite Integral \(\displaystyle \int \frac{x^3+x+1}{x^4+x^2+1}dx\) and \(\displaystyle \int \frac{x^2+x}{(e^x+x+1)^2}dx\)
by jacks
Thu Jul 14, 2016 6:59 am
Forum: Calculus
Topic: Indefinite Integrals
Replies: 2
Views: 581

Re: Indefinite Integrals

Thanks Apostolos J. Kos for Nice explanation.
by jacks
Thu Jul 14, 2016 6:56 am
Forum: Calculus
Topic: Indefinite Integrals
Replies: 2
Views: 581

Indefinite Integrals

Evaluation of Integrals \(\displaystyle (a):: \int\frac{1}{\left(2+\cos x\right)^2}dx\) and \(\displaystyle (b):: \int\frac{1}{\left(2+\cos x\right)^3}dx\)
by jacks
Wed Jul 13, 2016 9:03 am
Forum: Real Analysis
Topic: Infinite Series
Replies: 2
Views: 585

Infinite Series

Calculation of \(\displaystyle \lim_{n\rightarrow \infty}\prod_{r=1}^{n} \left(1+\frac{r}{n}\right)^{\frac{1}{n}}\)

Can we solve the above limit using Stirling approximation OR by using Stolz-Cesaro Theorem.

Thanks