What is the integral of x^2tan(x^3) ?

The integral of x^2tan(x^3) is -1/3 ln|cos(x^3)|+C

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integral of x^2tan(x^3)

\int x^{2} tan (x^{3}) d x

- \frac{1}{3} ln cos (x^{3}) + C

Solution steps

\int x^{2} tan (x^{3}) d x

Apply u-substitution

: \int \frac{tan ( u )}{3} d u

= \int \frac{tan ( u )}{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 tan (u) d u

Rewrite using trig identities

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

Apply u-substitution

: \int - \frac{1}{v} d v

= \frac{1}{3} \cdot \int - \frac{1}{v} d v

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{3} (- ln ∣ v ∣)

Substitute back

= \frac{1}{3} (- ln cos (x^{3}))

Simplify

= - \frac{1}{3} ln cos (x^{3})

Add a constant to the solution

= - \frac{1}{3} ln cos (x^{3}) + C

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\frac{( 1 - s ^{- 6} ) ^{2}}{( 1 - s ^{- 1} ) ^{2}}

\frac{\partial}{\partial y} (x z ln (x + y + z))

\frac{d ^{2}}{d x ^{2}} (5 cos (2 x + 10))

q \to 18 lim (0.9 q^{2} - 6 q + 80)

What is the integral of x^2tan(x^3) ?
The integral of x^2tan(x^3) is -1/3 ln|cos(x^3)|+C