Ответ:

[tex]\int {tg}^{4} (x + 3)dx[/tex]

[tex]\int {tg}^{4} (x + 3) \times \frac{1}{1} dt[/tex]

[tex]\int {tg}^{4} (x + 3) \times 1dt[/tex]

[tex]\int {tg}^{4} (x + 3)dt[/tex]

[tex]\int {tg}^{4} (t)dt[/tex]

[tex] \frac{1}{4 - 1} \times {tg}^{4 - 1} (t) - \int {tg}^{4 - 2} (t)dt[/tex]

[tex] \frac{1}{3} \times {tg}^{3} (t) - \int {tg}^{2} (t)dt[/tex]

[tex] \frac{1}{3} \times {tg}^{3} (t) - \int {sec}^{2} (t) - 1dt[/tex]

[tex] \frac{1}{3} \times {tg}^{3} (t) - (\int {sec}^{2} (t)dt - \int1dt)[/tex]

[tex] \frac{1}{3} \times {tg}^{3} (t) - (tg(t) - t)[/tex]

[tex] \frac{1}{3} \times {tg}^{3} (x + 3) - (tg(x + 3) - (x + 3))[/tex]

[tex] \frac{ {tg}^{3}(x + 3) }{3} - (tg(x + 3) - x - 3)[/tex]

[tex] \frac{ {tg}^{3}(x + 3) }{3} - tg(x + 3) + x + 3[/tex]

[tex] \frac{ {tg}^{3} (x + 3)}{3} - tg(x + 3) + x + 3 + C, C\in\R[/tex]

[tex] \frac{ {tg}^{3} (x + 3)}{3} - tg(x + 3) + x + C, C\in\R[/tex]