Evaluate
∫ 40 x + 40 5 x 2 + 10 x + 4 d x \displaystyle \int\frac{{{40}{x}+{40}}}{{{5}{x}^{{2}}+{10}{x}+{4}}}{\left.{d}{x}\right.} ∫ 5 x 2 + 10 x + 4 40 x + 40 d x where
5 x 2 + 10 x + 4 > 0 \displaystyle {5}{x}^{{2}}+{10}{x}+{4}>{0} 5 x 2 + 10 x + 4 > 0 .
First substitute u =
Preview Question 6 Part 1 of 4
Then
∫ 40 x + 40 5 x 2 + 10 x + 4 d x = ∫ \displaystyle \int\frac{{{40}{x}+{40}}}{{{5}{x}^{{2}}+{10}{x}+{4}}}{\left.{d}{x}\right.}=\int ∫ 5 x 2 + 10 x + 4 40 x + 40 d x = ∫ Preview Question 6 Part 2 of 4
du
Now integrate with respect to u to get
Preview Question 6 Part 3 of 4
+ C
So
∫ 40 x + 40 5 x 2 + 10 x + 4 d x \displaystyle \int\frac{{{40}{x}+{40}}}{{{5}{x}^{{2}}+{10}{x}+{4}}}{\left.{d}{x}\right.} ∫ 5 x 2 + 10 x + 4 40 x + 40 d x =
Preview Question 6 Part 4 of 4
+ C
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Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c