Solve 73 1+cos alpha 5 -sin alpha 5 ; 1-cos alpha 5 -sin alpha 5 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\int \frac { 1 + \cos ^ { 2 } \frac { 1 } { 6 } - \sin ^ { 2 } \frac { 1 } { 6 } } { 1 - \cos \frac { 4 } { 5 } \cdot \sin \frac { 1 } { 5 } }$$

Evaluate

$\frac{499995769214436079167302341594867411x}{296932475000000000000000000}+С$

Solution Steps

Evaluate trigonometric functions in the problem

$$\int {\frac{1 + 0.9999957692054863 ^ {2} - 0.002908877984361934 ^ {2}}{1 - 0.9999999988122701}} dx$$

Calculate $0.9999957692054863$ to the power of $2$ and get $0.99999153842887222221715401948769$.

$$\int \frac{1+0.99999153842887222221715401948769-0.002908877984361934^{2}}{1-0.9999999988122701}\mathrm{d}x$$

Add $1$ and $0.99999153842887222221715401948769$ to get $1.99999153842887222221715401948769$.

$$\int \frac{1.99999153842887222221715401948769-0.002908877984361934^{2}}{1-0.9999999988122701}\mathrm{d}x$$

Calculate $0.002908877984361934$ to the power of $2$ and get $0.000008461571127905547944653108220356$.

$$\int \frac{1.99999153842887222221715401948769-0.000008461571127905547944653108220356}{1-0.9999999988122701}\mathrm{d}x$$

Subtract $0.000008461571127905547944653108220356$ from $1.99999153842887222221715401948769$ to get $1.999983076857744316669209366379469644$.

$$\int \frac{1.999983076857744316669209366379469644}{1-0.9999999988122701}\mathrm{d}x$$

Subtract $0.9999999988122701$ from $1$ to get $0.0000000011877299$.

$$\int \frac{1.999983076857744316669209366379469644}{0.0000000011877299}\mathrm{d}x$$

Expand $\frac{1.999983076857744316669209366379469644}{0.0000000011877299}$ by multiplying both numerator and the denominator by $1000000000000000000000000000000000000$.

$$\int \frac{1999983076857744316669209366379469644}{1187729900000000000000000000}\mathrm{d}x$$

Reduce the fraction $\frac{1999983076857744316669209366379469644}{1187729900000000000000000000}$ to lowest terms by extracting and canceling out $4$.

$$\int \frac{499995769214436079167302341594867411}{296932475000000000000000000}\mathrm{d}x$$

Find the integral of $\frac{499995769214436079167302341594867411}{296932475000000000000000000}$ using the table of common integrals rule $\int a\mathrm{d}x=ax$.

$$\frac{499995769214436079167302341594867411x}{296932475000000000000000000}$$

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.

$$\frac{499995769214436079167302341594867411x}{296932475000000000000000000}+С$$

Differentiate w.r.t. x

$\frac{499995769214436079167302341594867411}{296932475000000000000000000} = 1683870277\frac{2.858904932310593 \times 10^{26}}{2.9693247499999997 \times 10^{26}} = 1683870277.9628131$