What is the integral of (x+1)^{100} ?

The integral of (x+1)^{100} is ((x+1)^{101})/(101)+C

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integral of (x+1)^{100}

\int (x + 1)^{100} d x

\frac{( x + 1 ) ^{101}}{101} + C

Solution steps

\int (x + 1)^{100} d x

Apply u-substitution

: \int u^{100} d u

= \int u^{100} d u

Apply the Power Rule

: \frac{u ^{101}}{101}

= \frac{u ^{101}}{101}

Substitute back

u = x + 1

= \frac{( x + 1 ) ^{101}}{101}

Add a constant to the solution

= \frac{( x + 1 ) ^{101}}{101} + C

x \to 0 lim (x^{\frac{3}{2}})

e^{t - 7}

\int 2 + e^{2 t} + e^{- 2 t} d t

x^{2} + 5 x + 9

x \to 5 lim (x - 1)

What is the integral of (x+1)^{100} ?
The integral of (x+1)^{100} is ((x+1)^{101})/(101)+C