What is the integral of (5t^2+3t) ?

The integral of (5t^2+3t) is (5t^3)/3+(3t^2)/2+C

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integral of (5t^2+3t)

\int (5 t^{2} + 3 t) d t

\frac{5 t ^{3}}{3} + \frac{3 t ^{2}}{2} + C

Solution steps

\int 5 t^{2} + 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 5 t^{2} d t + \int 3 t d t

\int 5 t^{2} d t = \frac{5 t ^{3}}{3}

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

= \frac{5 t ^{3}}{3} + \frac{3 t ^{2}}{2}

Add a constant to the solution

= \frac{5 t ^{3}}{3} + \frac{3 t ^{2}}{2} + C

\frac{d}{d x} (sec (x))

6 x + 7, x, 0, 8

\int \frac{1}{( 4 x ^{2} - 9 ) ^{3}} d x

y^{^{'}} = 42 + 20 x + 42 y + 28 x y

What is the integral of (5t^2+3t) ?
The integral of (5t^2+3t) is (5t^3)/3+(3t^2)/2+C