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Popular >

integral of (5-15x^2)csc^2(x^3-x)

Solution

\int (5 - 15 x^{2}) csc^{2} (x^{3} - x) d x

Solution

5 cot (x^{3} - x) + C

Solution steps

\int (5 - 15 x^{2}) csc^{2} (x^{3} - x) d x

Apply u-substitution

: \int - 5 csc^{2} (u) d u

= \int - 5 csc^{2} (u) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 5 \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= - 5 (- cot (u))

Substitute back

u = x^{3} - x

= - 5 (- cot (x^{3} - x))

Simplify

= 5 cot (x^{3} - x)

Add a constant to the solution

= 5 cot (x^{3} - x) + C

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Frequently Asked Questions (FAQ)

What is the integral of (5-15x^2)csc^2(x^3-x) ?
The integral of (5-15x^2)csc^2(x^3-x) is 5cot(x^3-x)+C