What is the integral of 3^{2x^6}3x^5 ?

The integral of 3^{2x^6}3x^5 is 729/2 x^6+C

integral of 3^{2x^6}3x^5

\int 3^{2 x^{6}} 3 x^{5} d x

\frac{729}{2} x^{6} + C

Solution steps

\int 3^{2 x^{6}} \cdot 3 x^{5} d x

Take the constant out:

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

= 3 \cdot \int 3^{2 x^{6}} x^{5} d x

3^{2 x^{6}} = 9^{x^{6}}

= 3 \cdot \int 9^{x^{6}} x^{5} d x

Apply u-substitution

= 3 \cdot \int \frac{243}{2} d u

Integral of a constant:

\int a d x = a x

= 3 \cdot \frac{243}{2} u

Substitute back

u = x^{6}

= 3 \cdot \frac{243}{2} x^{6}

Simplify

3 \cdot \frac{243}{2} x^{6} : \frac{729}{2} x^{6}

= \frac{729}{2} x^{6}

Add a constant to the solution

= \frac{729}{2} x^{6} + C

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What is the integral of 3^{2x^6}3x^5 ?
The integral of 3^{2x^6}3x^5 is 729/2 x^6+C