What is the integral of 3xsec^2(4)x^2 ?

The integral of 3xsec^2(4)x^2 is (3sec^2(4)x^4)/4+C

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integral of 3xsec^2(4)x^2

\int 3 x sec^{2} (4) x^{2} d x

\frac{3 sec ^{2} ( 4 ) x ^{4}}{4} + C

Solution steps

\int 3 x sec^{2} (4) x^{2} d x

Take the constant out:

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

= 3 sec^{2} (4) \cdot \int x x^{2} d x

Simplify

x x^{2} : x^{3}

= 3 sec^{2} (4) \cdot \int x^{3} d x

Apply the Power Rule

= 3 sec^{2} (4) \frac{x ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 sec ^{2} ( 4 ) x ^{4}}{4}

Add a constant to the solution

= \frac{3 sec ^{2} ( 4 ) x ^{4}}{4} + C

What is the integral of 3xsec^2(4)x^2 ?
The integral of 3xsec^2(4)x^2 is (3sec^2(4)x^4)/4+C