What is the integral of 15sqrt(x+1) ?

The integral of 15sqrt(x+1) is 10(x+1)^{3/2}+C

Popular >

integral of 15sqrt(x+1)

\int 15 x + 1 d x

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

Solution steps

\int 15 x + 1 d x

Take the constant out:

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

= 15 \cdot \int x + 1 d x

Apply u-substitution

: \int u d u

= 15 \cdot \int u d u

Apply the Power Rule

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

= 15 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x + 1

= 15 \cdot \frac{2}{3} (x + 1)^{\frac{3}{2}}

Simplify

15 \cdot \frac{2}{3} (x + 1)^{\frac{3}{2}} : 10 (x + 1)^{\frac{3}{2}}

= 10 (x + 1)^{\frac{3}{2}}

Add a constant to the solution

= 10 (x + 1)^{\frac{3}{2}} + C

e^{x} y \frac{d y}{d x} = 1

y = \frac{2}{x}, (- 2, - 1)

\int \frac{x}{2 x ^{3}} d x

x \to 1 lim (5 x^{5} - 8 x^{3} + 8)

\int 3 sin (4 x) + 4 sin (3 x) d x

What is the integral of 15sqrt(x+1) ?
The integral of 15sqrt(x+1) is 10(x+1)^{3/2}+C