Recent content by Mariuszek

If you want to get u substitution for ths integrals draw a curve y^2=ax^2+bx+c and cut it with secant line If secant line intersects curve at (λ,0) or (μ,0) you will get third substitution If secant line intersects curve at (0,\sqrt{c}) or (0,−\sqrt{c}) you will get second substitution Assume...

\int{\sec^{3}{\theta}\mbox{d}\theta} If you use u=\csc{\theta} substitution you will have to do the partial fraction decomposition u=\sec{\theta}+\tan{\theta} will also work If you prefer reduction formula use it

Furthermore use sqeeze theorem to calculate \lim_{x\to 0}{\frac{\sin{x}}{x}} L'Hospital rule will not work in that limit

Professional translation will cost you approximately 61 USD or 41 GBP I doubt that automatized translators are able to translate this because pdf was made from image file If you want to try rewrite it manually to doc file

if you pay for it you can find people able to translate it People are like this Automatized translations are not good quality I would translate it from polish to english but my english is not good

Inverse trig substitution not always is a good substitution for integrals with square root of quadratic f.e \int{\frac{\mbox{d}x}{x\sqrt{2x^2-2x+1}}}\\\int{\frac{\mbox{d}x}{x\sqrt{2x^2-2x-1}}}\\\int{\frac{\mbox{d}x}{x^2\left(4x^2-3\right)^2\sqrt{x^2-1}}} If you want to get u substitution for...

If you are able to speak russian there is some explanation of geometrical meaning If you prefer polish language I can also send pdf in this language

Draw a curve y2=ax2+bx+c Cut it with secant line If you choose proper points you will get second and third substitution If you cut the curve with line parallel to asymptote you will get first substitution

It is quite easy to find russian and polish version