What is the integral of x^2sin(xz) ?

The integral of x^2sin(xz) is -xcos(xz)+C

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integral of x^2sin(xz)

\int x^{2} sin (x z) d z

- x cos (x z) + C

Solution steps

\int x^{2} sin (x z) d z

Take the constant out:

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

= x^{2} \cdot \int sin (x z) d z

Apply u-substitution

: \int \frac{sin ( u )}{x} d u

= x^{2} \cdot \int \frac{sin ( u )}{x} d u

Take the constant out:

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

= x^{2} \frac{1}{x} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= x^{2} \frac{1}{x} (- cos (u))

Substitute back

u = x z

= x^{2} \frac{1}{x} (- cos (x z))

Simplify

x^{2} \frac{1}{x} (- cos (x z)) : - x cos (x z)

= - x cos (x z)

Add a constant to the solution

= - x cos (x z) + C

x \to 0 lim (\frac{x + 2 - 2}{2 x + 5 - 3})

\int cos (x) \cdot sin^{3} (x) d x

\frac{d}{d x} (\frac{1}{x ^{2} cos ( x )})

y^{^{'}} = 135 y x^{4}

f (x) = (5 x^{3} + 2) (3 x^{3} + 2)