(\integral\_{}^{}\frac{5(x^{6} + 1)}{x^{2} + 1}dx) = | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt

$\int_{}^{}\frac{5(x^{6} + 1)}{x^{2} + 1}dx$ =

5(x⁷ + x)tan^–1x + Cq

x⁵ – $\frac{5}{3}$ x³ + 5x +c

3x⁴ – 5x² + 15x + c

5tan^–1 (x² + 1) + log(x² + 1) + c

Answer

x⁵ – $\frac{5}{3}$ x³ + 5x +c

Explanation

dx = $\int \frac { 5 \left( x ^ { 2 } + 1 \right) \left( x ^ { 4 } - x ^ { 2 } + 1 \right) } { \left( x ^ { 2 } + 1 \right) } d x$

= $\int 5 \left( x ^ { 4 } - x ^ { 2 } + 1 \right) d x$ = x⁵ – $\frac { 5 } { 3 } x ^ { 3 }$ + 5x + c

Question: \(\int_{}^{}\frac{5(x^{6} + 1)}{x^{2} + 1}dx\) =...