What is the integral of 6x^5(x^6)^5 ?

The integral of 6x^5(x^6)^5 is (x^{36})/6+C

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integral of 6x^5(x^6)^5

\int 6 x^{5} (x^{6})^{5} d x

\frac{x ^{36}}{6} + C

Solution steps

\int 6 x^{5} (x^{6})^{5} d x

Take the constant out:

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

= 6 \cdot \int x^{5} (x^{6})^{5} d x

Simplify

x^{5} (x^{6})^{5} : x^{35}

= 6 \cdot \int x^{35} d x

Apply the Power Rule

: \frac{x ^{36}}{36}

= 6 \cdot \frac{x ^{36}}{36}

Simplify

6 \cdot \frac{x ^{36}}{36} : \frac{x ^{36}}{6}

= \frac{x ^{36}}{6}

Add a constant to the solution

= \frac{x ^{36}}{6} + C

\int \frac{3 t ^{2} + 2}{( t ^{3} + 2 t + 3 ) ^{5}} d t

\frac{\partial}{\partial y} (cos (x + y))

\frac{d}{d x} (36 - x^{2})

\frac{\partial}{\partial x} (y^{4} cos (4 x))

\frac{\partial}{\partial x} (e^{(x y)})

What is the integral of 6x^5(x^6)^5 ?
The integral of 6x^5(x^6)^5 is (x^{36})/6+C