4
2 3 / 2 \ 4*tan (3*x)*asin(2*x)
asin (2*x)*tan (3*x)*\12 + 12*tan (3*x)/ + ---------------------
__________
/ 2
\/ 1 - 4*x
$$\left(12 \tan^{2}{\left(3 x \right)} + 12\right) \tan^{3}{\left(3 x \right)} \operatorname{asin}^{2}{\left(2 x \right)} + \frac{4 \tan^{4}{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
/ / 2 \ \
2 | 2 / 1 2*x*asin(2*x)\ 2 / 2 \ / 2 \ 24*\1 + tan (3*x)/*asin(2*x)*tan(3*x)|
4*tan (3*x)*|2*tan (3*x)*|- --------- + -------------| + 9*asin (2*x)*\1 + tan (3*x)/*\3 + 5*tan (3*x)/ + -------------------------------------|
| | 2 3/2| __________ |
| | -1 + 4*x / 2\ | / 2 |
\ \ \1 - 4*x / / \/ 1 - 4*x /
$$4 \left(2 \left(\frac{2 x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \tan^{2}{\left(3 x \right)} + 9 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(5 \tan^{2}{\left(3 x \right)} + 3\right) \operatorname{asin}^{2}{\left(2 x \right)} + \frac{24 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \tan^{2}{\left(3 x \right)}$$
/ / 2 \ / 2 \ / 2 \ / 2 \ \
| 3 | asin(2*x) 6*x 12*x *asin(2*x)| 2 / 2 \ | 4 / 2 \ 2 / 2 \| 2 / 2 \ / 1 2*x*asin(2*x)\ 54*\1 + tan (3*x)/*\3 + 5*tan (3*x)/*asin(2*x)*tan(3*x)|
8*|2*tan (3*x)*|------------- + ------------ + ---------------| + 27*asin (2*x)*\1 + tan (3*x)/*\2*tan (3*x) + 3*\1 + tan (3*x)/ + 10*tan (3*x)*\1 + tan (3*x)// + 36*tan (3*x)*\1 + tan (3*x)/*|- --------- + -------------| + -------------------------------------------------------|*tan(3*x)
| | 3/2 2 5/2 | | 2 3/2| __________ |
| |/ 2\ / 2\ / 2\ | | -1 + 4*x / 2\ | / 2 |
\ \\1 - 4*x / \-1 + 4*x / \1 - 4*x / / \ \1 - 4*x / / \/ 1 - 4*x /
$$8 \left(36 \left(\frac{2 x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan^{2}{\left(3 x \right)} + 27 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} + 10 \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan^{2}{\left(3 x \right)} + 2 \tan^{4}{\left(3 x \right)}\right) \operatorname{asin}^{2}{\left(2 x \right)} + 2 \left(\frac{12 x^{2} \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{6 x}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) \tan^{3}{\left(3 x \right)} + \frac{54 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(5 \tan^{2}{\left(3 x \right)} + 3\right) \tan{\left(3 x \right)} \operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \tan{\left(3 x \right)}$$