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Evaluate the integral. (Use C for the constant of integration.)
cos(x) (8 + 7 sin^2(x)) dx

Sagot :

JeanaShupp

Answer: [tex]8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Step-by-step explanation:

Consider [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx[/tex]

Substitute  t= sinx

then dt = cos x dx

[tex]\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C[/tex]

[tex][\int x^ndx=\dfrac{x^{n+1}}{n+1}+C][/tex]

[tex]=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

Hence, [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]

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