$\bf \displaystyle \int~\cfrac{sec^2(x)}{\sqrt{1+tan(x)}}\cdot dx\\\\
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u=1+tan(x)\implies \cfrac{du}{dx}=sec^2(x)\implies \cfrac{du}{sec^2(x)}=dx\\\\
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\displaystyle \int~\cfrac{\underline{sec^2(x)}}{\sqrt{u}}\cdot\cfrac{du}{\underline{sec^2(x)}}\implies \int~\cfrac{1}{\sqrt{u}}\cdot du\implies \int~u^{-\frac{1}{2}}\cdot du
\\\\\\
2u^{\frac{1}{2}}\implies 2\sqrt{1+tan(x)}+C$

6 0

2 years ago

Read 2 more answers

Which ordered pair represents a point on a line y = 2x +1. a. 0,3 b. 1,2 c. 2,1 d. -1,-1.

Drupady [299]

D. -1,-1 because If you were to place that on a graph you would get d. for your answer and you can also do it on a TI-83 plus calculator

4 0

2 years ago

A central angle θ in a circle with a radius of 6.4 centimeters intercepts an arc with a length of 8 centimeters. What is the rad

vlada-n [284]

Radius of the circle = r = 6.4 cm
Length of the arc = s = 8 cm
Measure of angle formed by the arc = θ = ?

The radius of the circle, arc length and the angle made by the arc at the center of the circle are related by the equation:

s = rθ

From here we can find θ by:

θ = s/r

Using the values, we get:

θ = 8/6.4

θ= 1.25 radians

Thus the radian measure of the angle θ made by the arc will be 1.25 radians

7 0

2 years ago

What is 3logy−2logx−4logz written as a single logarithm?

777dan777 [17]

Answer:

log $\frac{y^{3}}{x^{2} z^{4} }$