Issolvi ∫ (4/sqrt[5]{t}+3/t^6)dt

$$\int ( \frac { 4 } { \sqrt[ 5 ] { t } } + \frac { 3 } { t ^ { 6 } } ) d t$$

Evalwa

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}+С$$

Passi tas-Soluzzjonijiet

Tintegra s-somma terminu b'terminu.

$$\int \frac{4}{\sqrt[5]{t}}\mathrm{d}t+\int \frac{3}{t^{6}}\mathrm{d}t$$

Iffattura ‘l barra l-kostanti f’kull wieħed minn dawn it-termini.

$$4\int \frac{1}{\sqrt[5]{t}}\mathrm{d}t+3\int \frac{1}{t^{6}}\mathrm{d}t$$

Erġa' ikteb \frac{1}{\sqrt[5]{t}} bħala t^{-\frac{1}{5}}. Minn \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int t^{-\frac{1}{5}}\mathrm{d}t ma' \frac{t^{\frac{4}{5}}}{\frac{4}{5}}. Issimplifika. Immultiplika 4 b'\frac{5t^{\frac{4}{5}}}{4}.

$$5t^{\frac{4}{5}}+3\int \frac{1}{t^{6}}\mathrm{d}t$$

Minn \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int \frac{1}{t^{6}}\mathrm{d}t ma' -\frac{1}{5t^{5}}. Immultiplika 3 b'-\frac{1}{5t^{5}}.

$$5t^{\frac{4}{5}}-\frac{\frac{3}{t^{5}}}{5}$$

Issimplifika.

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}$$

Jekk F\left(t\right) huwa antiderivattiv ta' f\left(t\right), allura s-sett tal-antiderivati kollha ta' f\left(t\right) jingħata minn F\left(t\right)+C. Għalhekk, żid il-kostanti ta' integrazzjoni C\in \mathrm{R} mar-riżultat.

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}+С$$

Iddifferenzja w.r.t. t

$$\frac{4}{\sqrt[5]{t}}+\frac{3}{t^{6}}$$