T23

Najděte primitivní funkce:

\( \int \frac{dx}{x+a} , substituce u = x+a, du = 1dx \) integrate dx / (x+a)

\( \int (2x − 3)^{10} \,dx , subtituce u = (2x - 3), du = 1/2 dx \) T294 integrate (2x - 3)^10 dx

\( \int \sqrt[3]{1 - 3x} \,dx \) integrate cuberoot(1 - 3x) dx T295

\( \int \frac{ \,dx} { 4 + 9x^2 } \) integrate 1 / (4 + 9x^2 ) dx T296

\( \int (\sin 5x − \sin 5\alpha) \,dx \) integrate sin 5x - sin 5a dx

\( \int \frac{dx}{\sin^2 (2x + \frac{\pi}{4} } \) integrate 1 / sin^2 (2x + pi/4) dx

\( \int \sin^2 x \,dx \) integrate sin^2 x dx mocninu sin^2 x stáhnout na sin/cos 2x a pak pou6ít subtituci T299

\( \int \frac{x \,dx}{ 3 − 2x^2} \) integrate x / (3 - 2x^2) dx

\( \int \frac{x \,dx}{(1 + x^2)^2}, u = 1+x^2, du = 2x dx \) integrate x / ( (1 + x^2)^2 ) dx

\( \int \frac{x \,dx}{4 + x^4} \) dvě substituce: u1 = x^2, pak u2 = u/2 \) druhá substituce arctan x d/dx= 1/(1+x^2) x / (4 + x^4) dx T302

\( \int \frac{ \,dx }{ e^x + e^{−x} } \) integrate 1 / (e^x + e^-x) dx

\( \int \tan x \,dx \) integrate tan x dx

\( \int \cot x \,dx \) integrate cot x dx

\( \int \frac{cos^3 x}{\sin x} \,dx \) integrate cos^3 x / sin x dx