Category: Integration

Question Number 151501 by talminator2856791 last updated on 21/Aug/21 $$$$$$\int (\log x+1)x^{x}dx$$$$$$ Answered by puissant last updated on 21/Aug/21 $${K}=\int\left(\mathrm{1}+{lnx}\right){x}^{{x}}…

Question Number 151492 by talminator2856791 last updated on 21/Aug/21 $$$$$${\int }_0^1\frac{\tan (x^2+1)}{x^2+1}dx$$$$$$ Terms of Service Privacy Policy…

Question Number 20404 by Yozzzzy last updated on 26/Aug/17 $${\int }_0^{\pi /4}tan\left(\theta \right)ln(1-tan\left(\theta \right))d\theta =?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 20389 by tammi last updated on 26/Aug/17 $$\int \sin {}^{4}xdx$$ Answered by Joel577 last updated on 26/Aug/17 $$I=\int {\left(\frac{1-\cos 2x}{2}\right)}^{2}dx$$$$\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\int\:\left(\mathrm{1}\:−\:\mathrm{2cos}\:\mathrm{2}{x}\:+\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\right)\:{dx}…

Question Number 20387 by tammi last updated on 26/Aug/17 $$\int \sin px\cos qxdx$$ Answered by mrW1 last updated on 26/Aug/17 $$\sin (\mathrm{p}+\mathrm{q})\mathrm{x}=\sin \mathrm{px}\cos \mathrm{qx}+\cos \mathrm{px}\sin \mathrm{qx}$$$$\sin (\mathrm{p}-\mathrm{q})\mathrm{x}=\sin \mathrm{px}\cos \mathrm{qx}-\cos \mathrm{px}\sin \mathrm{qx}$$$$\Rightarrow\mathrm{sin}\:\mathrm{px}\:\mathrm{cos}\:\mathrm{qx}=\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{sin}\:\left(\mathrm{p}+\mathrm{q}\right)\mathrm{x}+\mathrm{sin}\:\left(\mathrm{p}−\mathrm{q}\right)\mathrm{x}\right] \…