Question

Find integration:

$\huge\mathtt\green{ \int{ c o s e c } ^ { 2 } x - 5 x + \sin x ) d x }$
Answer with proper explanation.

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Answer 1

Answer:

$-cotx - \frac{5x^{2} }{2} - cosx + C$

Step-by-step explanation:

Using the standard formulas

$\int\ {cosec^{2} x} \, dx = - cotx\\\int\ {x} \, dx = \frac{x^{2} }{2}\\ \int\ sin{x} \, dx = -cosx$

and also

$\int\ [f({x}) + g(x)]dx = \int\ f({x}) \, dx + \int\ g({x}) \, dx$ ,

we can clearly see that

$\int\ {cosec^{2} x} -5x +sinx \, dx$ =  $-cotx - \frac{5x^{2} }{2} - cosx + C$

WARNING: Never forget the +C !