-4 + x
1 + ------------------
_______________ _______________
/ 2 / 2
\/ x - 8*x + 17 \/ x - 8*x + 17 (-4 + x)*atan(x - 4)
------------------ - -------------------------- + --------------------
2 _______________ _______________
1 + (x - 4) / 2 / 2
x - 4 + \/ x - 8*x + 17 \/ x - 8*x + 17
$$\frac{\left(x - 4\right) \operatorname{atan}{\left(x - 4 \right)}}{\sqrt{x^{2} - 8 x + 17}} - \frac{\frac{x - 4}{\sqrt{x^{2} - 8 x + 17}} + 1}{x + \sqrt{x^{2} - 8 x + 17} - 4} + \frac{\sqrt{x^{2} - 8 x + 17}}{\left(x - 4\right)^{2} + 1}$$
2
/ -4 + x \ 2
|1 + ------------------| (-4 + x)
| _______________| -1 + ------------- _______________
| / 2 | 2 2 / 2
\ \/ 17 + x - 8*x / atan(-4 + x) 17 + x - 8*x (-4 + x) *atan(-4 + x) 2*\/ 17 + x - 8*x *(-4 + x) 2*(-4 + x)
------------------------------ + ------------------ + ------------------------------------------------ - ---------------------- - ----------------------------- + ----------------------------------
2 _______________ / _______________\ _______________ 3/2 2 _______________
/ _______________\ / 2 | / 2 | / 2 / 2 \ / 2\ / 2\ / 2
| / 2 | \/ 17 + x - 8*x \-4 + x + \/ 17 + x - 8*x /*\/ 17 + x - 8*x \17 + x - 8*x/ \1 + (-4 + x) / \1 + (-4 + x) /*\/ 17 + x - 8*x
\-4 + x + \/ 17 + x - 8*x /
$$- \frac{\left(x - 4\right)^{2} \operatorname{atan}{\left(x - 4 \right)}}{\left(x^{2} - 8 x + 17\right)^{\frac{3}{2}}} - \frac{2 \left(x - 4\right) \sqrt{x^{2} - 8 x + 17}}{\left(\left(x - 4\right)^{2} + 1\right)^{2}} + \frac{\left(\frac{x - 4}{\sqrt{x^{2} - 8 x + 17}} + 1\right)^{2}}{\left(x + \sqrt{x^{2} - 8 x + 17} - 4\right)^{2}} + \frac{\operatorname{atan}{\left(x - 4 \right)}}{\sqrt{x^{2} - 8 x + 17}} + \frac{2 \left(x - 4\right)}{\left(\left(x - 4\right)^{2} + 1\right) \sqrt{x^{2} - 8 x + 17}} + \frac{\frac{\left(x - 4\right)^{2}}{x^{2} - 8 x + 17} - 1}{\left(x + \sqrt{x^{2} - 8 x + 17} - 4\right) \sqrt{x^{2} - 8 x + 17}}$$
3 / 2 \
/ -4 + x \ / 2 \ / -4 + x \ | (-4 + x) |
2*|1 + ------------------| | (-4 + x) | 3*|1 + ------------------|*|-1 + -------------|
_______________ | _______________| _______________ 3*|-1 + -------------|*(-4 + x) | _______________| | 2 |
/ 2 | / 2 | 2 2 3 2 / 2 | 2 | | / 2 | \ 17 + x - 8*x/
2*\/ 17 + x - 8*x \ \/ 17 + x - 8*x / 3 6*(-4 + x) 3*(-4 + x) 3*(-4 + x)*atan(-4 + x) 3*(-4 + x) *atan(-4 + x) 8*(-4 + x) *\/ 17 + x - 8*x \ 17 + x - 8*x/ \ \/ 17 + x - 8*x /
- -------------------- - ------------------------------ + ---------------------------------- - ----------------------------------- - ---------------------------------- - ----------------------- + ------------------------ + ------------------------------ - ------------------------------------------------ - -------------------------------------------------
2 3 _______________ 2 _______________ 3/2 3/2 5/2 3 / _______________\ 3/2 2
/ 2\ / _______________\ / 2\ / 2 / 2\ / 2 / 2\ / 2 \ / 2 \ / 2 \ / 2\ | / 2 | / 2 \ / _______________\ _______________
\1 + (-4 + x) / | / 2 | \1 + (-4 + x) /*\/ 17 + x - 8*x \1 + (-4 + x) / *\/ 17 + x - 8*x \1 + (-4 + x) /*\17 + x - 8*x/ \17 + x - 8*x/ \17 + x - 8*x/ \1 + (-4 + x) / \-4 + x + \/ 17 + x - 8*x /*\17 + x - 8*x/ | / 2 | / 2
\-4 + x + \/ 17 + x - 8*x / \-4 + x + \/ 17 + x - 8*x / *\/ 17 + x - 8*x
$$\frac{8 \left(x - 4\right)^{2} \sqrt{x^{2} - 8 x + 17}}{\left(\left(x - 4\right)^{2} + 1\right)^{3}} - \frac{2 \left(\frac{x - 4}{\sqrt{x^{2} - 8 x + 17}} + 1\right)^{3}}{\left(x + \sqrt{x^{2} - 8 x + 17} - 4\right)^{3}} + \frac{3 \left(x - 4\right)^{3} \operatorname{atan}{\left(x - 4 \right)}}{\left(x^{2} - 8 x + 17\right)^{\frac{5}{2}}} - \frac{6 \left(x - 4\right)^{2}}{\left(\left(x - 4\right)^{2} + 1\right)^{2} \sqrt{x^{2} - 8 x + 17}} - \frac{3 \left(x - 4\right) \operatorname{atan}{\left(x - 4 \right)}}{\left(x^{2} - 8 x + 17\right)^{\frac{3}{2}}} - \frac{3 \left(\frac{x - 4}{\sqrt{x^{2} - 8 x + 17}} + 1\right) \left(\frac{\left(x - 4\right)^{2}}{x^{2} - 8 x + 17} - 1\right)}{\left(x + \sqrt{x^{2} - 8 x + 17} - 4\right)^{2} \sqrt{x^{2} - 8 x + 17}} - \frac{2 \sqrt{x^{2} - 8 x + 17}}{\left(\left(x - 4\right)^{2} + 1\right)^{2}} - \frac{3 \left(x - 4\right)^{2}}{\left(\left(x - 4\right)^{2} + 1\right) \left(x^{2} - 8 x + 17\right)^{\frac{3}{2}}} - \frac{3 \left(x - 4\right) \left(\frac{\left(x - 4\right)^{2}}{x^{2} - 8 x + 17} - 1\right)}{\left(x + \sqrt{x^{2} - 8 x + 17} - 4\right) \left(x^{2} - 8 x + 17\right)^{\frac{3}{2}}} + \frac{3}{\left(\left(x - 4\right)^{2} + 1\right) \sqrt{x^{2} - 8 x + 17}}$$