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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

Graph

Popular Examples

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\int \frac{2 y ^{4} + 6 y ^{2} - 1}{y ^{3} + 3 y} d y

integral of (y^3)/(1+9y^4)

\int \frac{y ^{3}}{1 + 9 y ^{4}} d y

integral of ln(a+x)

\int ln (a + x) d x

integral of 6tan(x)sec^5(x)

\int 6 tan (x) sec^{5} (x) d x

integral of (y^{1/3})/((y^{4/3)+9)^2}

\int \frac{y ^{\frac{1}{3}}}{( y ^{\frac{4}{3}} + 9 ) ^{2}} d y

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