Newbetuts

Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$

Evaluating $\int _0^1\frac{\ln ^2\left(x\right)\ln \left(1-x\right)}{1+x^2}\:dx$

Derivative of $\Gamma(t):=\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda$

Proof of a change-of-measure formula

If $f$ derivable on $[a,b]$ does $\int_a^t f'(x)dx=f(t)-f(a)$ true?

PDF of the difference between two independent beta random variables

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

If integration is a continuous analog of summation (Addition), what is the continuous analog of multiplication (Product)?

Applying the Fourier transform to Maxwell's equations

Evaluate $\int _0^1\int _0^1\int _0^1\int _0^1\sqrt{(z-w)^2+(x-y)^2} \, dw \, dz \, dy \, dx$

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Is $\int_{\mathbb{R}^2} e^{-u} \Delta u < \infty$?

Writing Integrals using Differential Forms

Integral Inequality $|\int_0^x f(t)dt|\le \frac{2}{81}\max_{0\le x\le1}|f^{''}(x)|$

A solution for $\int^{2\pi}_0e^{\cos \theta}\cos(a\theta -\sin \theta)\,d \theta $

Quaternion integration

Integral of $1 / \sqrt x$ using Limits

New posts in integration

Substitution for definite integrals

Dominated convergence theorem for complex-valued functions?

On the meaning of formal sums of $k$-cubes, i.e. $k$-chains (in integration on manifolds)

Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$

Evaluating $\int _0^1\frac{\ln ^2\left(x\right)\ln \left(1-x\right)}{1+x^2}\:dx$

Derivative of $\Gamma(t):=\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda$

Proof of a change-of-measure formula

If $f$ derivable on $[a,b]$ does $\int_a^t f'(x)dx=f(t)-f(a)$ true?

PDF of the difference between two independent beta random variables

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

If integration is a continuous analog of summation (Addition), what is the continuous analog of multiplication (Product)?

Applying the Fourier transform to Maxwell's equations

Evaluate $\int _0^1\int _0^1\int _0^1\int _0^1\sqrt{(z-w)^2+(x-y)^2} \, dw \, dz \, dy \, dx$

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Is $\int_{\mathbb{R}^2} e^{-u} \Delta u < \infty$?

Writing Integrals using Differential Forms

Integral Inequality $|\int_0^x f(t)dt|\le \frac{2}{81}\max_{0\le x\le1}|f^{''}(x)|$

A solution for $\int^{2\pi}_0e^{\cos \theta}\cos(a\theta -\sin \theta)\,d \theta $

Quaternion integration

Integral of $1 / \sqrt x$ using Limits