What is the integral of sin(x)cos^3(x)+1 ?

The integral of sin(x)cos^3(x)+1 is -(cos^4(x))/4+x+C

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integral of sin(x)cos^3(x)+1

\int sin (x) cos^{3} (x) + 1 d x

- \frac{cos ^{4} ( x )}{4} + x + C

Solution steps

\int sin (x) cos^{3} (x) + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (x) cos^{3} (x) d x + \int 1 d x

\int sin (x) cos^{3} (x) d x = - \frac{cos ^{4} ( x )}{4}

\int 1 d x = x

= - \frac{cos ^{4} ( x )}{4} + x

Add a constant to the solution

= - \frac{cos ^{4} ( x )}{4} + x + C

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What is the integral of sin(x)cos^3(x)+1 ?
The integral of sin(x)cos^3(x)+1 is -(cos^4(x))/4+x+C