Solve ∫ 225*tan(047x-1557)+665 wrt x

$$\int{ 225 \times \tan ( 047x-1557 ) +665 }d x$$

Evaluate

$$-225\tan(1557)x+665x+С$$

Solution Steps

Multiply 0 and 47 to get 0.

$$\int 225\tan(0x-1557)+665\mathrm{d}x$$

Anything times zero gives zero.

$$\int 225\tan(0-1557)+665\mathrm{d}x$$

Subtract 1557 from 0 to get -1557.

$$\int 225\tan(-1557)+665\mathrm{d}x$$

Find the integral of \frac{225\sin(-1557)}{\cos(-1557)}+665 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(\frac{225\sin(-1557)}{\cos(-1557)}+665\right)x$$

Simplify.

$$\left(-\frac{225\sin(1557)}{\cos(1557)}+665\right)x$$

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.

$$\left(-\frac{225\sin(1557)}{\cos(1557)}+665\right)x+С$$

Differentiate w.r.t. x

$$5\left(133-45\tan(1557)\right)$$