What is the integral of (1+x)^{0.5} ?

The integral of (1+x)^{0.5} is xsqrt(1+x)-0.5(0.66666…(1+x)^{3/2}-2sqrt(1+x))+C

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integral of (1+x)^{0.5}

integral

(1 + x)^{0.5}

x 1 + x - 0.5 (0.66666 \dots (1 + x)^{\frac{3}{2}} - 2 1 + x) + C

Solution steps

\int (1 + x)^{0.5} d x

Apply Integration By Parts

: x (1 + x)^{\frac{1}{2}} - \int \frac{0.5 x}{( 1 + x ) ^{\frac{1}{2}}} d x

= x (1 + x)^{\frac{1}{2}} - \int \frac{0.5 x}{( 1 + x ) ^{\frac{1}{2}}} d x

\int \frac{0.5 x}{( 1 + x ) ^{\frac{1}{2}}} d x = 0.5 (0.66666 \dots (1 + x)^{\frac{3}{2}} - 2 (1 + x)^{\frac{1}{2}})

= x (1 + x)^{\frac{1}{2}} - 0.5 (0.66666 \dots (1 + x)^{\frac{3}{2}} - 2 (1 + x)^{\frac{1}{2}})

Apply radical rule:

= x 1 + x - 0.5 (0.66666 \dots (1 + x)^{\frac{3}{2}} - 2 1 + x)

Add a constant to the solution

= x 1 + x - 0.5 (0.66666 \dots (1 + x)^{\frac{3}{2}} - 2 1 + x) + C

f (t) = e^{t} \cdot t^{\frac{1}{2}}

(x + 4 x - 5 i)^{3}

\frac{e ^{x}}{( e ) ^{2}} x + 1

\frac{1}{( 2 - y ^{2} )}

\frac{1}{( a + x ^{2} )}

What is the integral of (1+x)^{0.5} ?
The integral of (1+x)^{0.5} is xsqrt(1+x)-0.5(0.66666…(1+x)^{3/2}-2sqrt(1+x))+C