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Popular >

integral of t^3+t

Solution

\int t^{3} + t d t

Solution

\frac{t ^{4}}{4} + \frac{t ^{2}}{2} + C

Solution steps

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

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

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

= \frac{t ^{4}}{4} + \frac{t ^{2}}{2}

Add a constant to the solution

= \frac{t ^{4}}{4} + \frac{t ^{2}}{2} + C

Popular Examples

integral of y(1-y)

\int y (1 - y) d y

integral of 1/((x^2-2)(x^2+2))

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

integral of y/(ln(y))

\int \frac{y}{ln ( y )} d y

integral of e^x3x

\int e^{x} 3 x d x

integral of x^3sqrt(49+x^2)

\int x^{3} 49 + x^{2} d x

Frequently Asked Questions (FAQ)

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