What is the integral of 2t^3-6t+7 ?

The integral of 2t^3-6t+7 is (t^4)/2-3t^2+7t+C

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integral of 2t^3-6t+7

\int 2 t^{3} - 6 t + 7 d t

\frac{t ^{4}}{2} - 3 t^{2} + 7 t + C

Solution steps

\int 2 t^{3} - 6 t + 7 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^{3} d t - \int 6 t d t + \int 7 d t

\int 2 t^{3} d t = \frac{t ^{4}}{2}

\int 6 t d t = 3 t^{2}

\int 7 d t = 7 t

= \frac{t ^{4}}{2} - 3 t^{2} + 7 t

Add a constant to the solution

= \frac{t ^{4}}{2} - 3 t^{2} + 7 t + C

\frac{d}{d x} (\frac{14 x + 6 x ^{2}}{( 7 + 6 x ) ^{2}})

\frac{\partial}{\partial x} (\frac{- x - 7 y}{y ^{2} + 6 x ^{2}})

\frac{d}{d x} ((3 x + 2 y)^{5})

\int_{0}^{4} \frac{5}{2 x + 1} d x

3^{t}

What is the integral of 2t^3-6t+7 ?
The integral of 2t^3-6t+7 is (t^4)/2-3t^2+7t+C