What is the integral from 1 to 4 of cos(x)-3/(x^5) ?

The integral from 1 to 4 of cos(x)-3/(x^5) is sin(4)-sin(1)-765/1024

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integral from 1 to 4 of cos(x)-3/(x^5)

\int_{1}^{4} cos (x) - \frac{3}{x ^{5}} d x

sin (4) - sin (1) - \frac{765}{1024}

Decimal

- 2.34534 \dots

Solution steps

\int_{1}^{4} cos (x) - \frac{3}{x ^{5}} 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_{1}^{4} cos (x) d x - \int_{1}^{4} \frac{3}{x ^{5}} d x

\int_{1}^{4} cos (x) d x = sin (4) - sin (1)

\int_{1}^{4} \frac{3}{x ^{5}} d x = \frac{765}{1024}

= sin (4) - sin (1) - \frac{765}{1024}

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What is the integral from 1 to 4 of cos(x)-3/(x^5) ?
The integral from 1 to 4 of cos(x)-3/(x^5) is sin(4)-sin(1)-765/1024