What is the integral of (3x+1)^{sqrt(2)} ?

The integral of (3x+1)^{sqrt(2)} is (sqrt(2)-1)/3 (3x+1)^{sqrt(2)+1}+C

Popular >

integral of (3x+1)^{sqrt(2)}

\int (3 x + 1)^{2} d x

\frac{2 - 1}{3} (3 x + 1)^{2 + 1} + C

Solution steps

\int (3 x + 1)^{2} d x

Apply u-substitution

: \int \frac{u ^{2}}{3} d u

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

Apply the Power Rule

: (2 - 1) u^{2 + 1}

= \frac{1}{3} (2 - 1) u^{2 + 1}

Substitute back

u = 3 x + 1

= \frac{1}{3} (2 - 1) (3 x + 1)^{2 + 1}

Simplify

\frac{1}{3} (2 - 1) (3 x + 1)^{2 + 1} : \frac{2 - 1}{3} (3 x + 1)^{2 + 1}

= \frac{2 - 1}{3} (3 x + 1)^{2 + 1}

Add a constant to the solution

= \frac{2 - 1}{3} (3 x + 1)^{2 + 1} + C

sin^{2} (3 x)

t \to 1 lim (ln (t))

\frac{\partial}{\partial y} (x e^{y} + cos (y))

\frac{\partial}{\partial y} (\frac{3 x ^{2}}{y})

x \to 5 + lim (\frac{1}{( x - 5 ) ^{2}})

What is the integral of (3x+1)^{sqrt(2)} ?
The integral of (3x+1)^{sqrt(2)} is (sqrt(2)-1)/3 (3x+1)^{sqrt(2)+1}+C