What is the integral of x^2cos(x^3+5) ?

The integral of x^2cos(x^3+5) is 1/3 sin(x^3+5)+C

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integral of x^2cos(x^3+5)

\int x^{2} cos (x^{3} + 5) d x

\frac{1}{3} sin (x^{3} + 5) + C

Solution steps

\int x^{2} cos (x^{3} + 5) d x

Apply u-substitution

: \int \frac{u cos ( u ^{\frac{3}{2}} + 5 )}{2 x} d u

= \int \frac{cos ( u + 5 )}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int cos (u + 5) d u

Apply u-substitution

: \int cos (v) d v

= \frac{1}{3} \cdot \int cos (v) d v

Use the common integral:

\int cos (v) d v = sin (v)

= \frac{1}{3} sin (v)

Substitute back

= \frac{1}{3} sin (x^{3} + 5)

Add a constant to the solution

= \frac{1}{3} sin (x^{3} + 5) + C

\int \frac{x ^{3}}{1 + x ^{8}} d x

\frac{d}{d x} (\frac{1}{4} e^{- \frac{x}{2}})

x \to π lim (sin (x - π))

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

y^{^{'}} = \frac{4 x ^{2} + y ^{2}}{x y}

What is the integral of x^2cos(x^3+5) ?
The integral of x^2cos(x^3+5) is 1/3 sin(x^3+5)+C