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Question		Answer
wyraz wolny start learning		0
(x^n)' start learning		n*x^n-1
(x)' start learning		1
(a/x)' start learning		-a/x^2
(√x)' start learning		1/2√x
(a^x)' start learning		a^x*ln a
(e^x)' start learning		e^x
(log@ x)' start learning		1/x * ln a
(ln x)’ start learning		1/x
(sin x)' start learning		cos x
(cos x)' start learning		-sin x
(tg x)' start learning		1/cos^2 *x
(ctg x)' start learning		-1/sin^2 *x
(arcsin x)' start learning		1/√1√-x^2
(arccos x)' start learning		-1/√1-x^2
(arctg x)' start learning		1/x^2+1
(arcctg x)' start learning		-1/x^2+1
∫0 dx start learning		C
∫dx start learning		x + C
∫x dx start learning		1/2*x^2 + C
∫x^n dx start learning		1/n+1 * x^n+1 + C
∫c * f(x) dx start learning		c * ∫f(x) dx + C
∫sin x dx start learning		-cos x + C
∫cos x dx start learning		sin x + C
∫tg x dx start learning		-ln * \|cos x\| + C
∫ctg x dx start learning		ln * \|sin x\| + C
∫1/cos^2 x dx start learning		tg x + C
∫1/sin^2 x dx start learning		-ctg x + C
∫e^x dx start learning		e^x + C
∫a^x dx start learning		a^x/ln a + C
∫1/x^2+a^2 dx start learning		1/a * arctg x/a + C
∫1/x^2 - a^2 dx start learning		1/2a ln \|x-a/x+a\| + C
∫1/√x^2+a dx start learning		ln \|x+√x^2+a\| + C
∫[f(x) + g(x)] dx start learning		∫f(x) dx + ∫g(x) dx + C
∫e^ax dx start learning		1/a e^ax + C
∫sin(a*x) dx start learning		-1/a cos(x) + C
∫cos(a*x) dx start learning		1/a sin(x) + C

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