Question

Integrate sinx+2x with respect to x​

Answer 1

`→\int (\sin(x) + 2x)dx \\ = \int \sin(x)dx + 2 \int xdx \\ = - \cos(x) + 2.( \frac{ {x}^(2) }{2} ) +C\\ = \boxed{ {x}^(2) - \cos(x) + C}✓`

• x²-cos(x)+C is the right answer.

Answer 2

Use the half angle formula, sin^2(x) = 1/2*(1 - cos(2x)) and substitute into the integral so it becomes 1/2 times the integral of (1 - cos(2x)) dx. Set u = 2x and du = 2dx to perform u substitution on the integral. Since dx = du/2, the result is 1/4 times the integral of (1 - cos(u)

Explanation:

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