3.1 Integrals 1 to 100

\(\int \sqrt {1+2 x} \, dx\) [1]
\(\int x \sqrt {1+3 x} \, dx\) [2]
\(\int x^2 \sqrt {1+x} \, dx\) [3]
\(\int \genfrac {}{}{}{}{x}{\sqrt {2-3 x}} \, dx\) [4]
\(\int \genfrac {}{}{}{}{1+x}{(2+2 x+x^2)^3} \, dx\) [5]
\(\int \sin ^3(x) \, dx\) [6]
\(\int \sqrt [3]{-1+z} z \, dz\) [7]
\(\int \cot (x) \csc ^2(x) \, dx\) [8]
\(\int \cos (2 x) \sqrt {4-\sin (2 x)} \, dx\) [9]
\(\int \genfrac {}{}{}{}{\sin (x)}{(3+\cos (x))^2} \, dx\) [10]
\(\int \genfrac {}{}{}{}{\sin (x)}{\sqrt {\cos ^3(x)}} \, dx\) [11]
\(\int \genfrac {}{}{}{}{\sin (\sqrt {1+x})}{\sqrt {1+x}} \, dx\) [12]
\(\int x^{-1+n} \sin (x^n) \, dx\) [13]
\(\int \genfrac {}{}{}{}{x^5}{\sqrt {1-x^6}} \, dx\) [14]
\(\int t \sqrt [4]{1+t} \, dt\) [15]
\(\int \genfrac {}{}{}{}{1}{(1+x^2)^{3/2}} \, dx\) [16]
\(\int x^2 (27+8 x^3)^{2/3} \, dx\) [17]
\(\int \genfrac {}{}{}{}{\cos (x)+\sin (x)}{\sqrt [3]{-\cos (x)+\sin (x)}} \, dx\) [18]
\(\int \genfrac {}{}{}{}{x}{\sqrt {1+x^2+(1+x^2)^{3/2}}} \, dx\) [19]
\(\int \genfrac {}{}{}{}{x}{\sqrt {1+x^2} \sqrt {1+\sqrt {1+x^2}}} \, dx\) [20]
\(\int \genfrac {}{}{}{}{\sqrt [5]{1-2 x+x^2}}{1-x} \, dx\) [21]
\(\int x \sin (x) \, dx\) [22]
\(\int x^2 \sin (x) \, dx\) [23]
\(\int x^3 \cos (x) \, dx\) [24]
\(\int x^3 \sin (x) \, dx\) [25]
\(\int \cos (x) \sin (x) \, dx\) [26]
\(\int x \cos (x) \sin (x) \, dx\) [27]
\(\int \sin ^2(x) \, dx\) [28]
\(\int \sin ^3(x) \, dx\) [29]
\(\int \sin ^4(x) \, dx\) [30]
\(\int \sin ^5(x) \, dx\) [31]
\(\int \sin ^6(x) \, dx\) [32]
\(\int x \sin ^2(x) \, dx\) [33]
\(\int x \sin ^3(x) \, dx\) [34]
\(\int x^2 \sin ^2(x) \, dx\) [35]
\(\int \cos ^2(x) \, dx\) [36]
\(\int \cos ^3(x) \, dx\) [37]
\(\int \cos ^4(x) \, dx\) [38]
\(\int (a^2-x^2)^{5/2} \, dx\) [39]
\(\int \genfrac {}{}{}{}{x^5}{\sqrt {5+x^2}} \, dx\) [40]
\(\int \genfrac {}{}{}{}{t^3}{\sqrt {4+t^3}} \, dt\) [41]
\(\int \tan ^2(x) \, dx\) [42]
\(\int \tan ^4(x) \, dx\) [43]
\(\int \cot ^2(x) \, dx\) [44]
\(\int \cot ^4(x) \, dx\) [45]
\(\int (2+3 x) \sin (5 x) \, dx\) [46]
\(\int x \sqrt {1+x^2} \, dx\) [47]
\(\int x (-1+x^2)^9 \, dx\) [48]
\(\int \genfrac {}{}{}{}{3+2 x}{(7+6 x)^3} \, dx\) [49]
\(\int x^4 (1+x^5)^5 \, dx\) [50]
\(\int (1-x)^{20} x^4 \, dx\) [51]
\(\int \genfrac {}{}{}{}{\sin (\genfrac {}{}{}{}{1}{x})}{x^2} \, dx\) [52]
\(\int \sin (\sqrt [4]{-1+x}) \, dx\) [53]
\(\int x \cos (x^2) \sin (x^2) \, dx\) [54]
\(\int \sqrt {1+3 \cos ^2(x)} \sin (2 x) \, dx\) [55]
\(\int \genfrac {}{}{}{}{1}{2+3 x} \, dx\) [56]
\(\int \log ^2(x) \, dx\) [57]
\(\int x \log (x) \, dx\) [58]
\(\int x \log ^2(x) \, dx\) [59]
\(\int \genfrac {}{}{}{}{1}{1+t} \, dt\) [60]
\(\int \cot (x) \, dx\) [61]
\(\int x^n \log (a x) \, dx\) [62]
\(\int x^2 \log ^2(x) \, dx\) [63]
\(\int \genfrac {}{}{}{}{1}{x \log (x)} \, dx\) [64]
\(\int \genfrac {}{}{}{}{\log (1-t)}{1-t} \, dt\) [65]
\(\int \genfrac {}{}{}{}{\log (x)}{x \sqrt {1+\log (x)}} \, dx\) [66]
\(\int x^3 \log ^3(x) \, dx\) [67]
\(\int e^{x^3} x^2 \, dx\) [68]
\(\int \genfrac {}{}{}{}{2^{\sqrt {x}}}{\sqrt {x}} \, dx\) [69]
\(\int e^{2 \sin (x)} \cos (x) \, dx\) [70]
\(\int e^x \sin (x) \, dx\) [71]
\(\int e^x \cos (x) \, dx\) [72]
\(\int \genfrac {}{}{}{}{1}{1+e^x} \, dx\) [73]
\(\int e^x x \, dx\) [74]
\(\int e^{-x} x \, dx\) [75]
\(\int e^x x^2 \, dx\) [76]
\(\int e^{-2 x} x^2 \, dx\) [77]
\(\int e^{\sqrt {x}} \, dx\) [78]
\(\int e^{-x^2} x^3 \, dx\) [79]
\(\int e^{a x} \cos (b x) \, dx\) [80]
\(\int e^{a x} \sin (b x) \, dx\) [81]
\(\int \cot ^{-1}(x) \, dx\) [82]
\(\int \sec ^{-1}(x) \, dx\) [83]
\(\int \csc ^{-1}(x) \, dx\) [84]
\(\int \arcsin (x)^2 \, dx\) [85]
\(\int \genfrac {}{}{}{}{\arcsin (x)}{x^2} \, dx\) [86]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a^2-x^2}} \, dx\) [87]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-2 x-x^2}} \, dx\) [88]
\(\int \genfrac {}{}{}{}{1}{a^2+x^2} \, dx\) [89]
\(\int \genfrac {}{}{}{}{1}{a+b x^2} \, dx\) [90]
\(\int \genfrac {}{}{}{}{1}{2-x+x^2} \, dx\) [91]
\(\int x \arctan (x) \, dx\) [92]
\(\int x^2 \arccos (x) \, dx\) [93]
\(\int x \arctan (x)^2 \, dx\) [94]
\(\int \arctan (\sqrt {x}) \, dx\) [95]
\(\int \genfrac {}{}{}{}{\arctan (\sqrt {x})}{\sqrt {x} (1+x)} \, dx\) [96]
\(\int \sqrt {1-x^2} \, dx\) [97]
\(\int \genfrac {}{}{}{}{e^{\arctan (x)} x}{(1+x^2)^{3/2}} \, dx\) [98]
\(\int \genfrac {}{}{}{}{e^{\arctan (x)}}{(1+x^2)^{3/2}} \, dx\) [99]
\(\int \genfrac {}{}{}{}{x^2}{(1+x^2)^2} \, dx\) [100]