What is the integral of 2xsin(x^2)+1/(x^2)sin(1/x) ?

The integral of 2xsin(x^2)+1/(x^2)sin(1/x) is -cos(x^2)+cos(1/x)+C

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integral of 2xsin(x^2)+1/(x^2)sin(1/x)

\int 2 x sin (x^{2}) + \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

- cos (x^{2}) + cos (\frac{1}{x}) + C

Solution steps

\int 2 x sin (x^{2}) + \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x sin (x^{2}) d x + \int \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

\int 2 x sin (x^{2}) d x = - cos (x^{2})

\int \frac{1}{x ^{2}} sin (\frac{1}{x}) d x = cos (\frac{1}{x})

= - cos (x^{2}) + cos (\frac{1}{x})

Add a constant to the solution

= - cos (x^{2}) + cos (\frac{1}{x}) + C

y = \frac{7}{sin ( x ) + cos ( x )}, (0, 7)

\frac{d}{d x} (2^{3 x - 1})

y = \frac{x}{1 + x ^{2}}, (3, 0.3)

x \to 0 + lim (\frac{2}{x} - \frac{2}{∣ x ∣})

\frac{d}{d x} (c x e^{3 x})

What is the integral of 2xsin(x^2)+1/(x^2)sin(1/x) ?
The integral of 2xsin(x^2)+1/(x^2)sin(1/x) is -cos(x^2)+cos(1/x)+C