How do you find the following indefinite integral of $(x^{2} + sin (2 x)) d x$ $(x^(2)+sin(2x))dx$ ?

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How do you find the following indefinite integral of $(x^{2} + sin (2 x)) d x$ $(x^(2)+sin(2x))dx$ ?

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Answer 1 · 2015-08-26T21:40:50

I found: $\frac{x^{3}}{3} + {sin}^{2} (x) + c$ $x^3/3+sin^2(x)+c$

Explanation:

Consider:
$\int (x^{2} + sin (2 x)) d x =$ $int(x^2+sin(2x))dx=$
$\int x^{2} d x + \int sin (2 x) d x =$ $intx^2dx+intsin(2x)dx=$
$= \frac{x^{3}}{3} + \int 2 sin (x) cos (x) d x =$ $=x^3/3+int2sin(x)cos(x)dx=$ but $d [sin (x)] = cos (x) d x$ $d[sin(x)]=cos(x)dx$ ;
$x^3/3+2intsin(x)d[sin(x)]=x^3/3+cancel(2)sin^2(x)/cancel(2)+c$

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How do you find the following indefinite integral of $(x^{2} + sin (2 x)) d x$ $(x^(2)+sin(2x))dx$ ?

1 Answer

Explanation:

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How do you find the following indefinite integral of $(x^{2} + sin (2 x)) d x$ $(x^(2)+sin(2x))dx$ ?