Neodređeni integrali

 $\int\frac{x+1}{\sqrt{x\sqrt{x}}}dx$  

•  $\frac{4}{5}\cdot x^{\frac{5}{4}}+4\cdot x^{\frac{1}{4}}+C$  

•  $\frac{3}{4}\cdot x^{\frac{4}{3}}+3\cdot x^{\frac{1}{3}}+C$  

•  $4\cdot x^{\frac{5}{4}}+\frac{5}{4}\cdot x^{\frac{1}{4}}+C$  

•  $x^{\frac{1}{5}}+3\cdot x^{\frac{3}{4}}+C$  

 $\int\frac{x^3}{\sqrt{x^2-1}}dx$  

•  $\frac{1}{3}\cdot\left(x^2+2\right)\sqrt{x^2-1}+C$  

•  $\left(x^2+3\right)\sqrt{x^2-1}+C$  

•  $\frac{1}{2}\cdot\left(x^2-2\right)\sqrt{x^2-1}+C$  

•  $4\cdot\left(x^2-1\right)\sqrt{x^2-1}+C$  

 $\int\frac{dx}{\sqrt{4+2x-x^2}}$  

•  $\arcsin\ \frac{x-1}{\sqrt{5}}+C$  

•  $\frac{1}{2}\cdot\arcsin\ \frac{x-1}{\sqrt{5}}+C$  

•  $\arcsin\ \frac{1-x}{\sqrt{3}}+C$  

•  $\arcsin\ \frac{x-2}{\sqrt{3}}+C$  

 $\int\frac{4x-3}{x^2-4x+5}dx$  

•  $2\cdot\ln\left|x^2-4x+5\right|+5\cdot arc\ tg\left(x-2\right)+C$  

•  $3\cdot\ln\left|x^2+4x+5\right|+4\cdot arc\ tg\left(x-1\right)+C$  

•  $\frac{1}{2}\cdot\ln\left|x^2-4x-5\right|-3\cdot arc\ tg\left(x+3\right)+C$  

•  $\ln\left|x^2-4x+5\right|-5\cdot arc\ tg\left(x+3\right)+C$  

 $\int\frac{dx}{\left(x-1\right)^2\left(x^2+1\right)}$  

•  $-\frac{1}{2\left(x-1\right)}-\frac{1}{2}\cdot\ln\left|x-1\right|+\frac{1}{4}\cdot\ln\left|x^2+1\right|+C$  

•  $\frac{1}{2\left(x-1\right)}+\frac{1}{2}\cdot\ln\left|x-1\right|+\ln\left|x^2+1\right|+C$  

•  $\frac{1}{x-1}-\frac{1}{2\ln\left|x-1\right|}+\frac{1}{4}\cdot\ln\left|x^2+1\right|+C$  

•  $-\frac{1}{x-1}-\frac{1}{2}\cdot\ln\left|x-2\right|-\ln\left|x^2-1\right|+C$  

 $\int e^{2x+1}\cdot\cos x\ dx$  

•  $\frac{1}{5}\cdot e^{2x+1}\left(\sin x+2\cos x\right)+C$  

•  $\frac{1}{6}\cdot e^{2x+1}\cdot\left(\cos x+2\sin x\right)+C$  

•  $\frac{1}{5}\cdot e^{2x+1}\left(\cos x+2\sin x\right)+C$  

•  $\frac{1}{6}\cdot e^{2x+1}\left(\sin x+2\cos x\right)+C$  

 $\int\frac{dx}{4-5\sin x}$  

•  $-\frac{1}{3}\cdot\ln\left|2\cdot tg\ \frac{x}{2}-1\right|+\frac{1}{3}\cdot\ln\left|tg\ \frac{x}{2}-2\right|+C$  

•  $\frac{1}{5}\cdot\ln\left|tg\ \frac{x}{2}+1\right|-\frac{1}{3}\cdot\ln\left|3\cdot tg\ \frac{x}{2}-2\right|+C$  

•  $\ln\left|\ \frac{tg\ \frac{x}{2}-5}{tg\ \frac{x}{2}+3}\right|+C$  

•  $3\cdot\ln\left|2\cdot tg\ \frac{x}{2}-3\right|+\frac{1}{4}\cdot\ln\left|tg\ \frac{x}{2}-1\right|+C$  

 $\int_{ }^{ }x^2\sin xdx$  

•  $x^2\sin x+2x\cos x-2\sin x+C$  

•  $2\cos x+2x\sin x-x^2\cos x+C$  

•  $x\sin x+x\cos x-2x^2+C$  

•  $\cos x-2x\sin x+x^2\cos x+C$  

 $\int_{ }\ln\left(x^2+1\right)dx$  

•  $x\cdot\ln\left|x^2+1\right|-2x+2arc\ tgx+C$  

•  $\ln\left|x^2+1\right|+2x-arc\ tgx+C$  

•  $x\cdot\ln\left|x^2+1\right|+arc\ tgx+C$  

•  $2x-\ln\left|x^2+1\right|+arc\ tgx+C$