What is the integral of (1+2x)^{50} ?

The integral of (1+2x)^{50} is 1/102 (1+2x)^{51}+C

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integral of (1+2x)^{50}

\int (1 + 2 x)^{50} d x

\frac{1}{102} (1 + 2 x)^{51} + C

Solution steps

\int (1 + 2 x)^{50} d x

Apply u-substitution

= \int \frac{u ^{50}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{50} d u

Apply the Power Rule

= \frac{1}{2} \cdot \frac{u ^{51}}{51}

Substitute back

u = 1 + 2 x

= \frac{1}{2} \cdot \frac{( 1 + 2 x ) ^{51}}{51}

Simplify

\frac{1}{2} \cdot \frac{( 1 + 2 x ) ^{51}}{51} : \frac{1}{102} (1 + 2 x)^{51}

= \frac{1}{102} (1 + 2 x)^{51}

Add a constant to the solution

= \frac{1}{102} (1 + 2 x)^{51} + C

What is the integral of (1+2x)^{50} ?
The integral of (1+2x)^{50} is 1/102 (1+2x)^{51}+C