What is the integral from 0 to 1 of x^5(1+x^6)^5 ?

The integral from 0 to 1 of x^5(1+x^6)^5 is 7/4

Popular >

integral from 0 to 1 of x^5(1+x^6)^5

\int_{0}^{1} x^{5} (1 + x^{6})^{5} d x

\frac{7}{4}

Decimal

1.75

Solution steps

\int_{0}^{1} x^{5} (1 + x^{6})^{5} d x

Apply u-substitution

: \int_{1}^{2} \frac{u ^{5}}{6} d u

= \int_{1}^{2} \frac{u ^{5}}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{1}^{2} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{1}^{2}

= \frac{1}{6} [\frac{u ^{6}}{6}]_{1}^{2}

Compute the boundaries:

\frac{21}{2}

= \frac{1}{6} \cdot \frac{21}{2}

Simplify

= \frac{7}{4}

\int_{0}^{4} (2 x - 6) d x

\int_{1}^{e^{8}} \frac{10 ln ( x )}{x} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (n x) d x

\int_{1}^{x} tan (x) d x

\int_{- 1}^{3} (2 x + 3) - (x^{2}) d x

What is the integral from 0 to 1 of x^5(1+x^6)^5 ?
The integral from 0 to 1 of x^5(1+x^6)^5 is 7/4