Alapintegrálokra visszavezethető feladatok

$$\begin{array}{lll} 1) \frac {1}{3}x^3-6x+5\ln(x)+C &2) \... ...}+C &9) -\frac {1}{3}(5-2x)^{\frac {3}{2}}+C \\ \end{array}$$

$$\int \frac {f'(x)}{f(x)}dx=\ln\vert f(x)\vert$$

$$\begin{array}{lll} 10)\ln\vert 3+x^3\vert+C&11)\ln\vert\ln... ...^2(x)+C \\ 19)\frac {3}{4}\tg^{\frac {4}{3}}(x) \end{array}$$

Racionális törtfűggvények integráljai

$$20)\frac {3}{2}\int\frac {2x-2}{x^2-2x+10}+\frac {2}{9}\int\frac ... ...ac {3}{2}\ln\vert x^2-2x+10\vert+\frac {2}{3}\arctg(\frac {1}{3}x-\frac {1}{3})$$

$$\begin{array}{ll} 21)\ln\vert 1+x\vert+2\ln\vert x-3\vert+... ...(x)+C &28) \int(1+\tg^2(x)-1)dx=\tg(x)-x+C \\ \end{array}$$

Parciális integrálás

$$\begin{array}{lll} 29) -xe^{-x}-e^{-x}+C&30) \frac {1}{9}... ...c {1}{3}\frac {\ln\vert 1+2^{3x}\vert}{\ln(2)}+C \end{array}$$

$$37) (u=\frac {1}{2}(2x+2))\quad \frac {1}{4}(2x+2)\sqrt{3-2x-x^2}+2\arsh(\frac {1}{2}+\frac {x}{2})+C$$

$$\begin{array}{lll} 38)\frac {1}{4}(2x-2)\sqrt{5-2x+x^2}+2\... ...-2\sqrt{2}\ln\vert\sqrt{2}x+\sqrt{2x^2-8}\vert+C \end{array}$$

Vegyes feladatok

$$\begin{array}{ll} 41)\frac {1}{3}e^x-\frac {1}{9}\ln\vert ... ...ac {x}{2})\cos(\frac {x}{2})+\frac {3x}{8}+C\\ \end{array}$$

$$57)-\frac {1}{5}\sin(x)\cos^4(x)+\frac {1}{15}\cos^2(x)\sin(x)+\frac {2}{15}\sin(x)+C$$

$$\begin{array}{lll} 58)\frac {1}{5}(\cos(x)+2\sin(x))e^(x)\... ...59)^3\sqrt{\frac {1}{10}\cos^{10}(3x)}+C\\ \end{array}$$