What is the integral of 1.05(x+180)^{0.05} ?

The integral of 1.05(x+180)^{0.05} is 1(x+180)^{1.05}+C

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integral of 1.05(x+180)^{0.05}

\int 1.05 (x + 180)^{0.05} d x

1 (x + 180)^{1.05} + C

Solution steps

\int 1.05 (x + 180)^{0.05} d x

Take the constant out:

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

= 1.05 \cdot \int (x + 180)^{0.05} d x

Apply u-substitution

= 1.05 \cdot \int u^{0.05} d u

Apply the Power Rule

= 1.05 \cdot 0.95238 \dots u^{1.05}

Substitute back

u = x + 180

= 1.05 \cdot 0.95238 \dots (x + 180)^{1.05}

Simplify

= 1 (x + 180)^{1.05}

Add a constant to the solution

= 1 (x + 180)^{1.05} + C

What is the integral of 1.05(x+180)^{0.05} ?
The integral of 1.05(x+180)^{0.05} is 1(x+180)^{1.05}+C