Use a table of integrals to find the indefinite integral. ∫cos⁡xsin2x+1dx

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Use a table of integrals to find the indefinite integral.  ∫cos⁡xsin2x+1dx

Wendy Boykin · Accepted Answer

Step 1  Integration is summation of discrete data. The integral is calculated for the functions to find their area, displacement, volume, that occurs due to combination of small data.  Integration is of two types definite integral and indefinite integral. Indefinite integral are defined where upper and lower limits are not given, whereas in definite integral both upper and lower limit are there.  Step 2  The given integrand is ∫cos⁡xsin2x+1dx, let u=sin⁡x differentiate it with respect to x from both sides.   u=sin⁡x  dudx=dsin⁡xdx  dudx=cos⁡x  du=cos⁡xdx...(1)  Step 3  Now, substitute value of u=sin⁡x and du from equation (1) in ∫cos⁡xsin2x+1dx  ∫cos⁡xsin2x+1dx=∫duu2+1  =ln|u2+1+u|+C    (using ∫duu2+1=ln|u2+1+u|)  =ln|sin2(x)+1+sin⁡(x)|+C   (substitute u=sin⁡(x))  Therefore, value of ∫cos⁡xsin2x+1dx is equal to ln|sin2(x)+1+sin⁡(x)|+C

Edward Patten · Accepted Answer

∫cos⁡(x)sin2(x)+1dx  Substitution u=sin⁡(x)⇒dudx=cos⁡(x)⇒dx=1cos⁡(x)du:  =∫1u2+1du  Lets

nick1337 · Accepted Answer

Use a table of integrals to find the indefinite integral. \int

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