What is the integral of θtan(2)θ^2 ?

The integral of θtan(2)θ^2 is 1/4 tan(2)θ^4+C

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integral of θtan(2)θ^2

\int θ tan (2) θ^{2} d θ

\frac{1}{4} tan (2) θ^{4} + C

Solution steps

\int θ tan (2) θ^{2} d θ

Take the constant out:

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

= tan (2) \cdot \int θ θ^{2} d θ

Simplify

θ θ^{2} : θ^{3}

= tan (2) \cdot \int θ^{3} d θ

Apply the Power Rule

= tan (2) \frac{θ ^{4}}{4}

Simplify

tan (2) \frac{θ ^{4}}{4} : \frac{1}{4} tan (2) θ^{4}

= \frac{1}{4} tan (2) θ^{4}

Add a constant to the solution

= \frac{1}{4} tan (2) θ^{4} + C

What is the integral of θtan(2)θ^2 ?
The integral of θtan(2)θ^2 is 1/4 tan(2)θ^4+C