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Popular >

integral of 1/(sqrt(x(3+\sqrt{x)))}

Solution

\int \frac{1}{x ( 3 + x )} d x

Solution

4 3 + x + C

Solution steps

\int \frac{1}{x ( 3 + x )} d x

Apply u-substitution

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

= \int \frac{2}{3 + u} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{3 + u} d u

Apply u-substitution

: \int 2 d v

= 2 \cdot \int 2 d v

Integral of a constant:

\int a d x = a x

= 2 \cdot 2 v

Substitute back

= 2 \cdot 2 3 + x

Simplify

= 4 3 + x

Add a constant to the solution

= 4 3 + x + C

Popular Examples

integral of (-5x+1)

\int (- 5 x + 1) d x

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integral of (4y)/(sqrt(x^3))

\int \frac{4 y}{x ^{3}} d x

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

integral of 9x(4+3x)^5

\int 9 x (4 + 3 x)^{5} d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(sqrt(x(3+\sqrt{x)))} ?
The integral of 1/(sqrt(x(3+\sqrt{x)))} is 4sqrt(3+\sqrt{x)}+C