What is the integral of (3x+1)^5 ?

The integral of (3x+1)^5 is 1/18 (3x+1)^6+C

Popular >

integral of (3x+1)^5

\int (3 x + 1)^{5} d x

\frac{1}{18} (3 x + 1)^{6} + C

Solution steps

\int (3 x + 1)^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{3} d u

= \int \frac{u ^{5}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{3} \cdot \frac{u ^{6}}{6}

Substitute back

u = 3 x + 1

= \frac{1}{3} \cdot \frac{( 3 x + 1 ) ^{6}}{6}

Simplify

\frac{1}{3} \cdot \frac{( 3 x + 1 ) ^{6}}{6} : \frac{1}{18} (3 x + 1)^{6}

= \frac{1}{18} (3 x + 1)^{6}

Add a constant to the solution

= \frac{1}{18} (3 x + 1)^{6} + C

\frac{d}{d θ} (\frac{5}{9 sin ( θ ) + 7 cos ( θ )})

\frac{d}{d x} (3 (e^{x} + x e^{x}))

x^{2} - 4 x, 3 x, 0, 7

\int - 9 tan^{3} (x) d x

\int_{0}^{π} sec^{2} (\frac{π}{3}) d x