Solve the trigonometric integral int(7/((1+tan(x)^2)^(1/2)))dx

 Exercise

$\int\frac{7}{\sqrt{1+\tan^2x}}dx$

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Rewrite the trigonometric expression $\frac{7}{\sqrt{1+\tan\left(x\right)^2}}$ inside the integral

$\int\frac{7}{\sec\left(x\right)}dx$

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Applying the trigonometric identity: $\displaystyle\frac{1}{\sec(\theta)}=\cos(\theta)$

$\int7\cos\left(x\right)dx$

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The integral of a function times a constant ($7$) is equal to the constant times the integral of the function

$7\int\cos\left(x\right)dx$

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Apply the integral of the cosine function: $\int\cos(x)dx=\sin(x)$

$7\sin\left(x\right)$

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As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$7\sin\left(x\right)+C_0$

$7\sin\left(x\right)+C_0$

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