What is the integral of (2x+1)csc(x^2+x)cot(x^2+x) ?

The integral of (2x+1)csc(x^2+x)cot(x^2+x) is -csc(x^2+x)+C

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integral of (2x+1)csc(x^2+x)cot(x^2+x)

\int (2 x + 1) csc (x^{2} + x) cot (x^{2} + x) d x

- csc (x^{2} + x) + C

Solution steps

\int (2 x + 1) csc (x^{2} + x) cot (x^{2} + x) d x

Apply u-substitution

: \int csc (u) cot (u) d u

= \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \int - 1 d v

Integral of a constant:

\int a d x = a x

= (- 1) v

Substitute back

= (- 1) csc (x^{2} + x)

Simplify

= - csc (x^{2} + x)

Add a constant to the solution

= - csc (x^{2} + x) + C

\int 17 t e^{t} d t

\frac{d}{d x} (\frac{x ^{4}}{8} + \frac{1}{4 x ^{2}})

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

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{- 2 x}

n \to \infty lim (\frac{1}{5})

What is the integral of (2x+1)csc(x^2+x)cot(x^2+x) ?
The integral of (2x+1)csc(x^2+x)cot(x^2+x) is -csc(x^2+x)+C