T24
Metodou per partes najděte primitivní funkce:
\( (f g)' = f'g + f g' \) pak \( \int f g' dx = f g - \int f' g \)
307.
\( \int x \ln x \,dx \) integrate x ln x dx T307
308.
\( \int \ln x \,dx \) integrate ln x dx T308
309.
\( \int \sqrt{x} \ln^2 x \,dx \)
integrate sqrt x ln^2 x dx
310.
\( \int \frac{\ln^2 x}{x^2\sqrt{x}} \,dx \)
integrate (ln^2 x) / (x^2 sqrt x) dx
311.
\( \int \ln^2 x \,dx \) integrate ln^2 x dx
2krát per-partes: f = ln^x, dg = dx, df= 2 ln x 1/x dx, g = x, druhá stejná jako 307, viz T311
312.
\( \int xe^{−x} \,dx \) integrate x e^-x dx viz T312
313.
\( \int x \sin^2 x \,dx \)
integrate x sin^2 x dx
314.
\( \int x^2 \sin 2x \,dx \)
integrate x^2 sin 2x dx