What is the integral of (9+x^5)^7x^4 ?

The integral of (9+x^5)^7x^4 is 1/40 (9+x^5)^8+C

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integral of (9+x^5)^7x^4

\int (9 + x^{5})^{7} x^{4} d x

\frac{1}{40} (9 + x^{5})^{8} + C

Solution steps

\int (9 + x^{5})^{7} x^{4} d x

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{7}{8} u^{\frac{8}{7}}

= \frac{1}{35} \cdot \frac{7}{8} u^{\frac{8}{7}}

Substitute back

u = (9 + x^{5})^{7}

= \frac{1}{35} \cdot \frac{7}{8} ((9 + x^{5})^{7})^{\frac{8}{7}}

Simplify

\frac{1}{35} \cdot \frac{7}{8} ((9 + x^{5})^{7})^{\frac{8}{7}} : \frac{1}{40} (9 + x^{5})^{8}

= \frac{1}{40} (9 + x^{5})^{8}

Add a constant to the solution

= \frac{1}{40} (9 + x^{5})^{8} + C

x \to 3 + lim (2 x^{2} - 4)

(3 y^{2} + 4 x) d x + (2 y x) d y = 0

\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}

\frac{d}{d x} (\frac{( x - 1 ) ^{2}}{( x + 2 )})

\frac{d}{d v} (v^{2})

What is the integral of (9+x^5)^7x^4 ?
The integral of (9+x^5)^7x^4 is 1/40 (9+x^5)^8+C