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We know, if f(x) is odd, then $\int_{- a}^{a} f (x) d x = 0$

$∴ I = \int_{- 2}^{2} (xcos (x) + \sin (x) + 1) d x$

$= 0 + 0 + \int_{- 2}^{2} f (x) d x [∵ xsin (x) and \sin (x) are odd] = {[x]}_{- 2}^{2} = 4$

72.

$\int_{π}^{16 π} |\sin (x)| d x$ is equal to

73.

$\int \frac{\cos (2 x)}{\cos (x)} dx$ is equal to

74.

$\int \frac{\sin^{8} (x) - \cos^{8} (x)}{1 - 2 \sin^{2} (x) \cos^{2} (x)} dx$

75.

The value of $\int_{0}^{π} \sin^{50} (x) \cos^{49} (x) d x$ is

76.

$\int 2^{x} (f' (x) + f (x) \log (2)) dx$ is

77.

Evaluate the following integral

$\int_{- 1}^{2} |xsin (πx)| d x$

78.

$\int \frac{\log (\sqrt{x})}{3 x} dx$ is equal to

79.

$\int e^{x} (\frac{2}{x} - \frac{2}{x^{2}}) dx$

80.

The value of the integral $\int \frac{dx}{{(e^{x} + e^{- x})}^{2}}$