What is the integral of 15(x+2)^4 ?

The integral of 15(x+2)^4 is 3(x+2)^5+C

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integral of 15(x+2)^4

\int 15 (x + 2)^{4} d x

3 (x + 2)^{5} + C

Solution steps

\int 15 (x + 2)^{4} d x

Take the constant out:

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

= 15 \cdot \int (x + 2)^{4} d x

Apply u-substitution

: \int u^{4} d u

= 15 \cdot \int u^{4} d u

Apply the Power Rule

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

= 15 \cdot \frac{u ^{5}}{5}

Substitute back

u = x + 2

= 15 \cdot \frac{( x + 2 ) ^{5}}{5}

Simplify

15 \cdot \frac{( x + 2 ) ^{5}}{5} : 3 (x + 2)^{5}

= 3 (x + 2)^{5}

Add a constant to the solution

= 3 (x + 2)^{5} + C

y^{^{'}} = y (1 - y), y (0) = - 5

n = 0 \sum \infty \frac{1}{( 1 + n ) ^{2}}

\frac{d}{d x} (3 cos (3 x))

4 x^{\frac{5}{4}} + 10 x^{\frac{3}{2}} + 5 x

(1, - 2), (3, 1)