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

The integral of cos(t)+sin^3(t) is sin(t)-cos(t)+(cos^3(t))/3+C

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integral of cos(t)+sin^3(t)

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

sin (t) - cos (t) + \frac{cos ^{3} ( t )}{3} + C

Solution steps

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

Apply the Sum Rule:

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

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

\int cos (t) d t = sin (t)

\int sin^{3} (t) d t = - cos (t) + \frac{cos ^{3} ( t )}{3}

= sin (t) - cos (t) + \frac{cos ^{3} ( t )}{3}

Add a constant to the solution

= sin (t) - cos (t) + \frac{cos ^{3} ( t )}{3} + C

y^{^{'}} + \frac{6}{x ^{2}} y = x^{10} e^{\frac{6}{x}}

\int (x - 4) (x + 4) d x

\int \frac{( arctan ( x ) ) ^{6}}{x ^{2} + 1} d x

\int \frac{1}{( 81 + x ^{2} ) ^{2}} d x

y^{^{''}} - 6 y^{^{'}} + 9 y = 5 t^{- 1} e^{3 t}

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