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Popular >

integral of (z-3)^n

Solution

\int (z - 3)^{n} d z

Solution

\frac{( z - 3 ) ^{n + 1}}{n + 1} + C

Solution steps

\int (z - 3)^{n} d z

Apply u-substitution

: \int u^{n} d u

= \int u^{n} d u

Apply the Power Rule

: \frac{u ^{n + 1}}{n + 1}

= \frac{u ^{n + 1}}{n + 1}

Substitute back

u = z - 3

= \frac{( z - 3 ) ^{n + 1}}{n + 1}

Add a constant to the solution

= \frac{( z - 3 ) ^{n + 1}}{n + 1} + C

Popular Examples

integral from-1 to 1 of (7x^3-2x^2+5x-4)

\int_{- 1}^{1} (7 x^{3} - 2 x^{2} + 5 x - 4) d x

(dy)/(dx)=(2x+1)/(2y)

\frac{d y}{d x} = \frac{2 x + 1}{2 y}

derivative of f(x)= 1/(sqrt(x+3))derivative of

f (x) = \frac{1}{x + 3}

(sqrt(ln(x)))^'

(ln (x))^{^{'}}

(dy)/(dx)=(-3y)

\frac{d y}{d x} = (- 3 y)

Frequently Asked Questions (FAQ)

What is the integral of (z-3)^n ?
The integral of (z-3)^n is ((z-3)^{n+1})/(n+1)+C