Solve ∫ 1/(cos^2frac{1{2}+sinpi/2)}

$$\int \frac { 1 } { ( \cos ^ { 2 } \frac { 1 } { 2 } + \sin \frac { \pi } { 2 } ) }$$

Evaluate

$$\frac{100000000000000000000000000000000x}{199992384757819564210293775574369}+С$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\int {\frac{1}{{(0.9999619230641713 ^ {2} + \sin(\frac{\pi}{2}))}}} dx$$

Calculate 0.9999619230641713 to the power of 2 and get 0.99992384757819564210293775574369.

$$\int \frac{1}{0.99992384757819564210293775574369+\sin(\frac{\pi }{2})}\mathrm{d}x$$

Get the value of \sin(\frac{\pi }{2}) from trigonometric values table.

$$\int \frac{1}{0.99992384757819564210293775574369+1}\mathrm{d}x$$

Add 0.99992384757819564210293775574369 and 1 to get 1.99992384757819564210293775574369.

$$\int \frac{1}{1.99992384757819564210293775574369}\mathrm{d}x$$

Expand \frac{1}{1.99992384757819564210293775574369} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\int \frac{100000000000000000000000000000000}{199992384757819564210293775574369}\mathrm{d}x$$

Find the integral of \frac{100000000000000000000000000000000}{199992384757819564210293775574369} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{100000000000000000000000000000000x}{199992384757819564210293775574369}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{100000000000000000000000000000000x}{199992384757819564210293775574369}+С$$

Differentiate w.r.t. x

$$\frac{100000000000000000000000000000000}{199992384757819564210293775574369} = 0.5000190388303777$$