What is the integral of tsqrt(7t^2+12) ?

The integral of tsqrt(7t^2+12) is 1/21 (7t^2+12)^{3/2}+C

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integral of tsqrt(7t^2+12)

\int t 7 t^{2} + 12 d t

\frac{1}{21} (7 t^{2} + 12)^{\frac{3}{2}} + C

Solution steps

\int t 7 t^{2} + 12 d t

Apply u-substitution

: \int \frac{u}{14} d u

= \int \frac{u}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{14} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 7 t^{2} + 12

= \frac{1}{14} \cdot \frac{2}{3} (7 t^{2} + 12)^{\frac{3}{2}}

Simplify

\frac{1}{14} \cdot \frac{2}{3} (7 t^{2} + 12)^{\frac{3}{2}} : \frac{1}{21} (7 t^{2} + 12)^{\frac{3}{2}}

= \frac{1}{21} (7 t^{2} + 12)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{21} (7 t^{2} + 12)^{\frac{3}{2}} + C

x \to 1 lim (- x^{2} - 5 x + 6)

f (x) = e^{x} cos (2 x)

5 \cdot (t - 8) - 10 \cdot (t - 4)

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

\int x (x^{3} - \frac{2}{x ^{2}} + 6) d x

What is the integral of tsqrt(7t^2+12) ?
The integral of tsqrt(7t^2+12) is 1/21 (7t^2+12)^{3/2}+C