What is the integral of sqrt(2t)-cos(6t) ?

The integral of sqrt(2t)-cos(6t) is sqrt(2)tsqrt(t)-(sqrt(2))/3 t^{3/2}-1/6 sin(6t)+C

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integral of sqrt(2t)-cos(6t)

\int 2 t - cos (6 t) d t

2 t t - \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{6} sin (6 t) + C

Solution steps

\int 2 t - cos (6 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 2 t d t - \int cos (6 t) d t

\int 2 t d t = 2 t t - \frac{2}{3} t^{\frac{3}{2}}

\int cos (6 t) d t = \frac{1}{6} sin (6 t)

= 2 t t - \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{6} sin (6 t)

Add a constant to the solution

= 2 t t - \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{6} sin (6 t) + C

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What is the integral of sqrt(2t)-cos(6t) ?
The integral of sqrt(2t)-cos(6t) is sqrt(2)tsqrt(t)-(sqrt(2))/3 t^{3/2}-1/6 sin(6t)+C