What is the integral of (7-x)^{49} ?

The integral of (7-x)^{49} is -((7-x)^{50})/(50)+C

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integral of (7-x)^{49}

\int (7 - x)^{49} d x

- \frac{( 7 - x ) ^{50}}{50} + C

Solution steps

\int (7 - x)^{49} d x

Apply u-substitution

: \int - u^{49} d u

= \int - u^{49} d u

Take the constant out:

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

= - \int u^{49} d u

Apply the Power Rule

: \frac{u ^{50}}{50}

= - \frac{u ^{50}}{50}

Substitute back

u = 7 - x

= - \frac{( 7 - x ) ^{50}}{50}

Add a constant to the solution

= - \frac{( 7 - x ) ^{50}}{50} + C

\int (x^{2} + 2)^{2} d x

\int \frac{tan ^{2} ( x ) + sec ^{2} ( x )}{tan ( x )} d x

\int \frac{2 x}{x ^{4} + 1} d x

f (x) = 12 x^{3} - \frac{1}{x}

x^{2} + 2 x + 2

What is the integral of (7-x)^{49} ?
The integral of (7-x)^{49} is -((7-x)^{50})/(50)+C