query: How to compute $\int_0^\infty e^{-ax}cos(bx) dx $?
positive_passages.docid: 69124
positive_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
negative_passages.docid: 6483
negative_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 110343
negative_passages.text: Integrating $\rm x^ae^{-bx}$.
negative_passages.docid: 39798
negative_passages.text: Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
negative_passages.docid: 42758
negative_passages.text: How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
negative_passages.docid: 11757
negative_passages.text: How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
negative_passages.docid: 33155
negative_passages.text: Use residues to evaluate $\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x$, where $|a|<1$
negative_passages.docid: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
negative_passages.docid: 132000
negative_passages.text: Calculate $\int_0^\infty\frac{\sin x}xdx$ by integration of a suitable function along given paths
negative_passages.docid: 41372
negative_passages.text: Stuck on crucial step while computing $\int_{- \infty}^{\infty} e^{-t^2}dt$
negative_passages.docid: 117602
negative_passages.text: How to evaluate $\int \cot^2(x) \;\mathrm dx$?
negative_passages.docid: 84884
negative_passages.text: Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $
negative_passages.docid: 58475
negative_passages.text: Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
negative_passages.docid: 95426
negative_passages.text: How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
negative_passages.docid: 124445
negative_passages.text: Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
negative_passages.docid: 121071
negative_passages.text: Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
negative_passages.docid: 43484
negative_passages.text: Integration by parts: $\int e^{ax}\cos(bx)\,dx$