Zacky

 21 How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$? 15 Integral $\int_0^{2π} e^{e^{ix}} dx$ 13 How to calculate $\int_{0}^{\pi/2}x^2\sqrt{\cos (x)}dx$ 13 Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$? 11 Evaluate $\int_0^1 \frac{\operatorname{arctanh}^3(x)}{x}dx$

### Reputation (7,885)

 +30 Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$? +60 Evaluate the trigonometric integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2\theta \cos^2\theta}{(\cos^3 \theta+\sin^3\theta)^2} \, \mathrm{d}\theta$ +10 Integral $\int_0^\infty \frac{\arctan(x^2)}{x^4+x^2+1}dx$ +5 Integral $\int_0^\infty \frac{\arctan(x^2)}{x^4+x^2+1}dx$

### Questions (69)

 34 Relation between the roots of a function 33 Integral for the New Year $2019$! 30 Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$ 24 Integral $\int_0^1 \frac{dx}{\prod_{n=1}^\infty (1+x^n)}$ 20 Integral $\int_0^\infty \frac{\ln x}{(\pi^2+\ln^2 x)(1+x)^2} \frac{dx}{\sqrt x}$

### Tags (85)

 439 integration × 127 49 logarithms × 9 303 definite-integrals × 74 43 indefinite-integrals × 7 187 calculus × 37 37 real-analysis × 8 66 closed-form × 32 31 sequences-and-series × 14 51 improper-integrals × 13 20 trigonometry × 6

### Accounts (3)

 Mathematics 7,885 rep 11062 Music: Practice & Theory 126 rep 6 Signal Processing 106 rep 3