What is the integral of 7x^7(x^8+4)^6 ?

The integral of 7x^7(x^8+4)^6 is 1/8 (x^8+4)^7+C

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integral of 7x^7(x^8+4)^6

\int 7 x^{7} (x^{8} + 4)^{6} d x

\frac{1}{8} (x^{8} + 4)^{7} + C

Solution steps

\int 7 x^{7} (x^{8} + 4)^{6} d x

Take the constant out:

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

= 7 \cdot \int x^{7} (x^{8} + 4)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{8} d u

= 7 \cdot \int \frac{u ^{6}}{8} d u

Take the constant out:

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

= 7 \cdot \frac{1}{8} \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= 7 \cdot \frac{1}{8} \cdot \frac{u ^{7}}{7}

Substitute back

u = x^{8} + 4

= 7 \cdot \frac{1}{8} \cdot \frac{( x ^{8} + 4 ) ^{7}}{7}

Simplify

7 \cdot \frac{1}{8} \cdot \frac{( x ^{8} + 4 ) ^{7}}{7} : \frac{1}{8} (x^{8} + 4)^{7}

= \frac{1}{8} (x^{8} + 4)^{7}

Add a constant to the solution

= \frac{1}{8} (x^{8} + 4)^{7} + C

f (x) = 7 x sin (π x)

\int_{0}^{2} (x^{4} - 2 x^{3}) d x

\int cos^{5} (3 x) sin (3 x) d x

\frac{\partial}{\partial x} (\frac{4 x}{x ^{2} + y ^{2}})

x \to - 7 lim (2 x + 5)

What is the integral of 7x^7(x^8+4)^6 ?
The integral of 7x^7(x^8+4)^6 is 1/8 (x^8+4)^7+C