What is the integral of (1+4x)^{3/5} ?

The integral of (1+4x)^{3/5} is 5/32 (1+4x)^{8/5}+C

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integral of (1+4x)^{3/5}

\int (1 + 4 x)^{\frac{3}{5}} d x

\frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

Solution steps

\int (1 + 4 x)^{\frac{3}{5}} d x

Apply u-substitution

: \int \frac{u ^{\frac{3}{5}}}{4} d u

= \int \frac{u ^{\frac{3}{5}}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int u^{\frac{3}{5}} d u

Apply the Power Rule

: \frac{5}{8} u^{\frac{8}{5}}

= \frac{1}{4} \cdot \frac{5}{8} u^{\frac{8}{5}}

Substitute back

u = 1 + 4 x

= \frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}}

Simplify

\frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}} : \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

Add a constant to the solution

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

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What is the integral of (1+4x)^{3/5} ?
The integral of (1+4x)^{3/5} is 5/32 (1+4x)^{8/5}+C