3.1 Integrals 1 to 70
3.1.1 \(\int (c e+d e x)^3 (a+b \arctan (c+d x)) \, dx\) [1]
3.1.2 \(\int (c e+d e x)^2 (a+b \arctan (c+d x)) \, dx\) [2]
3.1.3 \(\int (c e+d e x) (a+b \arctan (c+d x)) \, dx\) [3]
3.1.4 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{c e+d e x} \, dx\) [4]
3.1.5 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{(c e+d e x)^2} \, dx\) [5]
3.1.6 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{(c e+d e x)^3} \, dx\) [6]
3.1.7 \(\int (c e+d e x)^3 (a+b \arctan (c+d x))^2 \, dx\) [7]
3.1.8 \(\int (c e+d e x)^2 (a+b \arctan (c+d x))^2 \, dx\) [8]
3.1.9 \(\int (c e+d e x) (a+b \arctan (c+d x))^2 \, dx\) [9]
3.1.10 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{c e+d e x} \, dx\) [10]
3.1.11 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{(c e+d e x)^2} \, dx\) [11]
3.1.12 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{(c e+d e x)^3} \, dx\) [12]
3.1.13 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{(c e+d e x)^4} \, dx\) [13]
3.1.14 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{(c e+d e x)^5} \, dx\) [14]
3.1.15 \(\int (c e+d e x)^2 (a+b \arctan (c+d x))^3 \, dx\) [15]
3.1.16 \(\int (c e+d e x) (a+b \arctan (c+d x))^3 \, dx\) [16]
3.1.17 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{c e+d e x} \, dx\) [17]
3.1.18 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{(c e+d e x)^2} \, dx\) [18]
3.1.19 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{(c e+d e x)^3} \, dx\) [19]
3.1.20 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{(c e+d e x)^4} \, dx\) [20]
3.1.21 \(\int \genfrac {}{}{}{}{\arctan (1+x)}{2+2 x} \, dx\) [21]
3.1.22 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{\genfrac {}{}{}{}{a d}{b}+d x} \, dx\) [22]
3.1.23 \(\int (a+b x)^2 \sqrt {\arctan (a+b x)} \, dx\) [23]
3.1.24 \(\int (e+f x)^3 (a+b \arctan (c+d x)) \, dx\) [24]
3.1.25 \(\int (e+f x)^2 (a+b \arctan (c+d x)) \, dx\) [25]
3.1.26 \(\int (e+f x) (a+b \arctan (c+d x)) \, dx\) [26]
3.1.27 \(\int (a+b \arctan (c+d x)) \, dx\) [27]
3.1.28 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{e+f x} \, dx\) [28]
3.1.29 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{(e+f x)^2} \, dx\) [29]
3.1.30 \(\int \genfrac {}{}{}{}{a+b \arctan (c+d x)}{(e+f x)^3} \, dx\) [30]
3.1.31 \(\int (e+f x)^2 (a+b \arctan (c+d x))^2 \, dx\) [31]
3.1.32 \(\int (e+f x) (a+b \arctan (c+d x))^2 \, dx\) [32]
3.1.33 \(\int (a+b \arctan (c+d x))^2 \, dx\) [33]
3.1.34 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{e+f x} \, dx\) [34]
3.1.35 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^2}{(e+f x)^2} \, dx\) [35]
3.1.36 \(\int (e+f x)^2 (a+b \arctan (c+d x))^3 \, dx\) [36]
3.1.37 \(\int (e+f x) (a+b \arctan (c+d x))^3 \, dx\) [37]
3.1.38 \(\int (a+b \arctan (c+d x))^3 \, dx\) [38]
3.1.39 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{e+f x} \, dx\) [39]
3.1.40 \(\int \genfrac {}{}{}{}{(a+b \arctan (c+d x))^3}{(e+f x)^2} \, dx\) [40]
3.1.41 \(\int (e+f x)^m (a+b \arctan (c+d x)) \, dx\) [41]
3.1.42 \(\int (e+f x)^m (a+b \arctan (c+d x))^2 \, dx\) [42]
3.1.43 \(\int (e+f x)^m (a+b \arctan (c+d x))^3 \, dx\) [43]
3.1.44 \(\int x^3 \arctan (a+b x) \, dx\) [44]
3.1.45 \(\int x^2 \arctan (a+b x) \, dx\) [45]
3.1.46 \(\int x \arctan (a+b x) \, dx\) [46]
3.1.47 \(\int \arctan (a+b x) \, dx\) [47]
3.1.48 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{x} \, dx\) [48]
3.1.49 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{x^2} \, dx\) [49]
3.1.50 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{x^3} \, dx\) [50]
3.1.51 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{x^4} \, dx\) [51]
3.1.52 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+d x^3} \, dx\) [52]
3.1.53 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+d x^2} \, dx\) [53]
3.1.54 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+d x} \, dx\) [54]
3.1.55 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+\genfrac {}{}{}{}{d}{x}} \, dx\) [55]
3.1.56 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+\genfrac {}{}{}{}{d}{x^2}} \, dx\) [56]
3.1.57 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+\genfrac {}{}{}{}{d}{x^3}} \, dx\) [57]
3.1.58 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+d \sqrt {x}} \, dx\) [58]
3.1.59 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{c+\genfrac {}{}{}{}{d}{\sqrt {x}}} \, dx\) [59]
3.1.60 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{1+x^2} \, dx\) [60]
3.1.61 \(\int \genfrac {}{}{}{}{\arctan (d+e x)}{a+b x^2} \, dx\) [61]
3.1.62 \(\int \genfrac {}{}{}{}{\arctan (d+e x)}{a+b x+c x^2} \, dx\) [62]
3.1.63 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{\sqrt {1+a^2+2 a b x+b^2 x^2}} \, dx\) [63]
3.1.64 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{\sqrt {(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [64]
3.1.65 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{\sqrt [3]{1+a^2+2 a b x+b^2 x^2}} \, dx\) [65]
3.1.66 \(\int \genfrac {}{}{}{}{\arctan (a+b x)}{\sqrt [3]{(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [66]
3.1.67 \(\int \genfrac {}{}{}{}{(a+b x)^2 \arctan (a+b x)}{\sqrt {1+a^2+2 a b x+b^2 x^2}} \, dx\) [67]
3.1.68 \(\int \genfrac {}{}{}{}{(a+b x)^2 \arctan (a+b x)}{\sqrt {(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [68]
3.1.69 \(\int \genfrac {}{}{}{}{(a+b x)^2 \arctan (a+b x)}{\sqrt [3]{1+a^2+2 a b x+b^2 x^2}} \, dx\) [69]
3.1.70 \(\int \genfrac {}{}{}{}{(a+b x)^2 \arctan (a+b x)}{\sqrt [3]{(1+a^2) c+2 a b c x+b^2 c x^2}} \, dx\) [70]